I thought it might be interesting to have a variation on this thread;
My answer is never [in the last 15 years anyway]. Such an unpleasant experience with the traffic.
For most of my life I’ve either lived about 1.5 hours north and slightly east, or about 1.5 miles south and slightly west, of St. Louis. We drive through there a few times per year, to get from my home to Springfield (IL) where my family lives. Rarely do I go to St. Louis just to go to St. Louis; maybe three times in two years. When we have money, Mrs. H and I like to buy food at Soulard Farmers’ Market, and she loves to go to this Goodwill distribution center thing where you buy shit by the pound (the calls it “The Bins”).
I don’t particularly mourn the traffic in St. Louis - I know from driving in city traffic so it’s not a big deal. Parking is never really an issue in The Lou, either, if you’re there on the weekend and doing tourist things. The main thing that keeps from going there more often is the long drive. I’ve always hated long drives, and always will - and yes, to me (an American, no less!), a 1.5-hour drive is a long drive.
Not all cities have good mass transit but Chicago has a good train network. It’s pretty cheap too. It can still be a long ride in but just sleep or read or listen to music or watch videos or play games or talk with people. Just an all around more pleasant experience than sitting in traffic. Drops you off in the city-center too so from there an easy walk or taxi ride (or subway or bus) to your final destination.
A problem is that the out-of-towners are not familiar with the complexity of public transit systems.
Almost never.
I would love to go do things in the nearby big cities a few times a year. I could come up with an activity a week for a year if I tried
But a two hour drive, a few hours of walking around surrounded by people and probably awkward and expensive food. Followed by another two hour drive is a lot.
And I live with my eighty-ish parents, who are increasingly unable to enjoy the walking around looking at stuff part of the day.
And then there’s the other reality of being the only reasonably able-bodied adult, which means my days off often end up as chore days. Or doctor visit days.
I suppose one reason some people do it is for airplane connections: you can drive to the local airport an hour away but only connects to three cities or you can drive 4 hours to the big city which has direct flights to dozens of destinations–and the second is both cheaper and takes less total time than the first (the first having an additional layover).
Google seems to have this one sorted. Certainly the busses and subway will show as options when using Google maps. If you live nearby you might need to figure out the heavy rail schedules (I rarely take those in Chicago so find myself struggling with the schedule and which line and station but I get it figured out).
Jackson, Birmingham, and Memphis are all roughly two to two and a half hours away from where I live. I probably go to Jackson about once every couple of years, pretty much always for an event (political protest, state humanities council awards banquet). I’ve been to Memphis once. Birmingham never, except to the airport. I go to New York / DC / Chicago a lot more often than to any of them.
I probably should visit all of those cities sometime and see more of what they have to offer. The problem is that I hate driving, and I really hate driving in strange cities or on the interstate, and meanwhile our tiny regional airport is fifteen minutes away from where I live and a one-hour flight from Atlanta, where I can get an connecting flight to hundreds of interesting places, most of which have public transit.
Every few months, for bookstores, restaurants, parks, museums, or to see friends.
Since I relocated to southern Australia a couple of years ago, the only time I go anywhere near the capital city is to transit through to the international airport.
All the facilities found in the city are also available here in my (smallish) regional town, and I don’t relish crowds, so happy in my little bucolic backwood.
Your little town has numerous theaters (not movie theaters) and many restaurants and big museums and music and nightlife? (to name a few things)
Not that I’m one for ‘high-brow’ (LOL) activities, we do actually have a fair-dinkum theatre with various live performances, a gallery with regular exhibitions, pubs with live music, restaurants (none have made the Michelin guide yet of course) but no museum unless you count the little private ones that reflect upon the history of the town and hinterland.
If I suddenly develop a craving to head to the city for a bit of culture, the train runs three times a day, is a 3.5 hour journey each way, and it only costs app $5.00 return. So, it’s there, but I’m rather comfortable being a sloth really. 
Depending on traffic getting into said city, I’m less than 2hr from Montreal, ~3.5hr from Boston, and 7hr from Manhattan.
Lately, I’m probably in Montreal once a year on average, Boston much less (though I’ll be there twice this summer for two different concerts), and NYC maybe once every two years.
Montreal is great to go “just because”… have a vacation in a big city that is really easy to get to. Food, wandering, culture… it’s a very comfortable destination. We’ve also flown out of YUL on our way to other international destinations and it’s a lot more convenient and less expensive (most of the time) than using our local airport.
Boston I rarely go to, though I did a lot in my 20s when I had many friends going to college there. I still get slightly confused because I have sense memory of navigating into the city before the Big Dig. These days I’ve just been for some concerts. And I saw my first MLB game as an adult at Fenway in 2024.
NYC is mostly Broadway shows and food. Plus I’ve got a few close friends who live there. And museums sometimes.
I live an hour outside the city (New Orleans). Haven’t visited the city in months. I visit once a year if that.
I used to live in a small mining town and we’d go to the city 2-4 times a month to get supplies. It was a little over an hour drive or it was over 3 hours to get to Phoenix. This was mostly out of necessity however since the town had 1 basic grocer (Bashas’) and and only 2 restaurants (no franchises, locally owned).
I now live in the larger Phoenix metropolitan area, and to ask ‘How often do I visit Phoenix specifically?’ the answer would be virtually never. It’s an hour long drive and unless there is an event or driving thru, I’ve no other reason to go.
About once every 2-3 weeks, because that city is London and clients tend to congregate there. It’s normally just a working day trip though. I recently had to spend a week there for work, and can’t believe I actually lived there for almost 20 years. I now require green space, and lots of it to myself.
We live in a suburb in Los Angeles county. It’s about 2.5 hours to San Diego, and 4 hours to Las Vegas. We probably go to each of them about once per year. They both have attractions that Los Angeles does not, plus it’s good to get away from the local scene from time to time.