There’s a Shakey’s about 10 miles down the freeway, under an overpass next to a bowling alley. I stop there for the Bunch of Lunch every couple of years or so, as soon as I have forgotten the last time.
Just checked Wiki – sorry to see that the last Farrell’s Ice Cream Parlour Restaurant, in California, closed a few years ago. 
I originally came to the thread to throw a mention of Blake’s Lotaburger, a New Mexico icon, but I think they’ve juuust expanded enough to no longer qualify. They have 71 locations, all but 4 in New Mexico (2 in Tucson AZ, and 2 in El Paso Tx which is within 45 miles of NM, so maaaaay still count).
They’re a chain of old school burger places, where the burgers are cooked on griddles, and the staff wears paper hats still. Really good stuff if you like old school greasy burgers with grilled onions and green chili. Few perks, but solid good food. Growing up in Las Cruces, this is the chain everyone I knew went too, although in Southern NM, even the mega chains (McD and BK) had green chili burgers on the menu.
As a runner up choice that should still qualify, I’ll throw out Tumble 22 of Austin TX Fame. Nashville style hot chicken, 5 locations total, chicken ranges from wimpy > hot > mo’ hot! > dang hot!! > cluckin’ hot!!! > stupid hot!!! complete with illustrations… (advice, mo’ hot is best, hot enough to notice, no pain for me at least, dang hot if you are in the mood for some real burn, don’t… just don’t go higher).
I’m sure there are a lot of local pizza chains. In the Twin Cities (Minnesota) one such is Punch Pizza twelve locations (and growing). They’re wood-fired pizza specialists.
When visiting the Black Hills we ran across Boss’ Pizza & Chicken. We didn’t try the pizza, but the fried chicken was pretty good. The have a dozen locations, mostly in South Dakota but a few in North Dakota and Iowa and even Wisconsin.
We used to have a local Valentino’s Pizza that conveniently (for them) closed just as the pandemic started. They had a good by-the-slice special so they got lots of students and workers on their lunch break. It looks like they’ve contracted to their core Nebraska locations.
Black Bear Diner. Northern Cal and Nev. Kinda like an upscale Denny’s maybe? I dunno. Food is okay. Lot’s of bear decorations. That’s a bit tedious…
McMenamins. Most of their locations are in Oregon, though they have quite a few in Washington as well… maybe enough to disqualify them per the OP.
Their trademark is to take over older locations, and turn them into pubs/restaurants/hotels. Such as old churches, schools, and so on. Each one has some unique aspect to it. And the food is awesome.
My contribution here will be Burgermaster.
It’s a Seattle area fast food restaurant chain that’s been around since 1952. Their web site says they have 5 locations, all near Seattle, but there was a location way up north in Everett when I lived there and from what I can tell it’s still there and operating. 
So I don’t know how many they actually have.
Their burgers are great, as you’d expect. But I loved their Dungeness (crab) and Swiss on sourdough. It’s like a tuna melt, except with crab. Good luck finding that at another fast food place.
Also, for breakfast they used to have something called a Muffinmaster. It was the best breakfast sandwich I’ve ever had. Imagine if a gourmet chef made a sausage and egg McMuffin. Sadly, it looks like none of their locations do breakfast anymore, going by their online menus and restaurant hours.
Well known to locals, not at all known to outsiders.
Worth a visit for tourists, because their burger meat includes horse.
Whenever I visit Texas I always have to go to Taco Cabana. Good Mexican fast(ish) food!
Oh. Uhh, interesting.
Neigh to that.
mmm
Seattle’s got quite a few local chains.
Probably the most famous is Dick’s, a chain of walk-up huts (and one dine-in location) that serve inexpensive, McDonalds-ish burgers and fries and are open late at night. The menu essentially hasn’t changed since the early '70s and is very small - six burgers (plain, plain with cheese, ketchup and mustard, ketchup and mustard with cheese, tartar sauce and lettuce, and double patty tartar sauce and lettuce with cheese), one size of fries, fountain drinks, shakes, and ice cream. They don’t accept special orders because everything is already ready before you reach the counter and the cashier hands it to you within seconds of your paying for it, and you have to pay extra if you want condiment packets or a portion cup of chopped onions to add to your burger. Lines are usually long but move quickly, and you might even bump into Bill Gates while you’re waiting your turn.
Then there’s Ivar’s, a fish-and-chips chain that’s pretty good quality for fast food and also operates three full-service restaurants with a more elaborate fine dining menu.
For pizza there’s Pagliacci, which emphasizes using local ingredients, has a rotating seasonal menu, and features a lot of very unique signature pies and toppings you wouldn’t expect to find on a pizza. Their pizza crust is bland and uninteresting to me, but they also make amazing calzones and have their own in-house brand of gelato.
Further south you’ve got Burgerville, a Portland-based chain with locations around NE Oregon and SW Washington. They also focus on local ingredients and seasonal vegetables and have a cult following similar to In-n-Out.
Here in Olympia we have a chain that just barely counts called Eagan’s. They started in the '40s and peaked at 11 locations in the early '70s, but lost a lot of ground after McDonald’s and Burger King moved into town and now only have three locations, two under the Eagan’s name and one (the original location) which has been owned independently since the '60s and is instead called “Big Tom” after the chain’s signature double cheeseburger. What makes them unique is their use of “Goop”, a special sauce the founder’s mother invented in 1949, made of mayo, “salad dressing” (I.e. off-brand Miracle Whip), yellow mustard, and sweet relish, which tops their burgers and hot dogs and is also offered as a dipping sauce for fries, and is often imitated by other independent burger restaurants around the region. (Even the “tartar sauce” offered at Dick’s is actually a version of Goop.)
I don’t miss a lot about Seattle after moving away several years ago, but the regular opportunity to eat a big bag of Dick’s is near the top of the list.
In Seattle, “go eat a bag of Dick’s” isn’t an insult. 
Forgot to mention one - Ezell’s. Southern-style fried chicken, somewhat similar to Popeye’s but better. Oprah loves the stuff and has it flown out to Chicago when she’s in the mood for it.
I’ve read about Cook Out online and looked at the menu on their website several times, and they intrigue me. I’ll have a Big Double Burger tray, Cook Out style, add tomato and pickles, with rings, a corn dog, and a large Cheerwine, please.
I like Ivar’s - good for a quick cup of chowder as well as the seafood, when we are visiting Seattle.
Ha, that’s my go-to breakfast spot. I didn’t realize it was a chain.
I’ve visited several of their locations over the years – in addition to the one near my house, one is near my in-laws, and one is near the office where I worked for several years.
Aida (or Aïda) is an Austrian café chain. In addition to coffee, they serve cakes and pastries, breakfasts, light lunches, and (in the summer) ice cream. The staff all wear pink uniforms.
What I like best about them is their menu which has diagrams (on page 3) showing the composition of their various coffee drinks. If you’ve ever wondered what the difference is between a ristretto, espresso, latte, café au lait, cappuccino, melange, etc., then this diagram is a godsend.
The next-best thing about Aida is that every location has a big chart on the wall showing the baking schedule. They bake all their pastries on location, and so you can use the chart to time your visit such that your favourite type of pastry is just coming out of the oven.
Apart from the pastries, the foods they serve are pretty good. The lunches are nothing out of the ordinary (hot tuna sandwiches and the like) but of good quality. In summer time they usually have a few creative ice cream flavours, such as apple strudel.
If there’s a downside to Aida, it’s that the locations in central Vienna tend to be quite crowded, mostly but not entirely with tourists. Getting a seat is sometimes a problem; when you do you’ll often be elbow-to-elbow with other guests, and there will be a long wait before they take your order (and again before you can pay your bill).
Let’s see, continuing Chicago area, we have Fontano’s subs, for decent Italian submarine sandwiches.
Al’s for beef and Italian sausages various hot dog stand-type items. The only location, IMHO, worth going to is the original on Taylor Street.
Harold’s Chicken Shack for fried chicken (though there is considerable variation from chicken shack to chicken shack, and much argument over which is the best location. Here’s one ranking for those in the area who might be interested.
Baba’s Famous Steak and Lemonade for Philly cheesesteak-type and other beef sandwiches, and very sweet lemonade. I’m not sure how much of a formal chain it is. The branding seems to be the same on many of these, but there doesn’t seem to be one central website. There’s a bunch on the South Side here, but they either don’t have websites or each have individual ones. There’s also ones that call themselves “Baba’s Steak and Lemonade” without the “Famous”, and the “Baba’s” logo is not consistent across all locations calling themselves “Baba’s.” Lots of weird stuff happens on the South Side with businesses with very similar names or flat-out stealing another name with a slight change, but that one above has three locations, though not in Chicago proper (where is where I’ve always had Baba’s.)
Lou Malnati’s, of course, for pizza – known specifically for classic deep dish (not stuffed like Giordano’s, another local chain.) Lou’s is a perfectly good introduction to deep dish – get the sausage; Chicago is not really a pepperoni town. They have a smattering of locations in Arizona (of course–a number of Chicago places have outposts there. Like Rosati’s), Indiana, and Wisconsin.
Going next door to Northwest Indiana, we have Schoop Hamburgers. Some locations in Illinois, but mostly NW Indiana. Go to the Munster location. There is also considerable variation in quality here. Known for their crispy-edged, thin, fast food/diner style hamburgers.