This may be basic stuff. But it probably is relevant and businesses need to take care of the basics.
Unless they’re in really good condition, don’t get your hopes too high. My wife and last year took a bunch of my parents’ and her mother’s old LPs to a used vinyl store much like the OP is talking about opening. (The owner has a law practice, and runs the store out of the top floor of his office). Out of about 50 albums, he bought maybe four (and one of those was a collection of German polkas recorded at a Pennsylvania county fair, that I think he bought purely for the WTF factor). We thought he would be most interested in our copy of Gordon Lightfoot’s Sundown and the Beach Boys’ Pet Sounds, but he turned them both down due to wear and tear on the sleeves and the records. Turns out that vintage records are like those old Star Wars action figures you had as a kid - only valuable if you never played with them.
As for the OP, it sounds to me like they really just want to hang out with like-minded music fans, so thirding the advice to take a part-time job at a record store; that seems like a much higher fun-to-drudgery ratio.
That’s disappointing. I just want the damn things out of my house; I don’t really care how much cash I get for them. But I don’t want to spend a couple hours carting them to a record store if they’re only going to buy a handful of them. Maybe I’ll just dump them in the garbage.
This is my concern as well. Just where is the OP going to get inventory? And by that I mean good inventory. You might be able to buy some stock from a nearby store that is going out of business… but then you’ll be stuck with a pile of records that sat in that store for 3 years with nobody buying them (the dregs, the releases that nobody wants)
You could try to buy people’s collections - but as has been said, the days of getting a pile of good vinyl for cheap are long gone. And you’re competing with the online hobbyists buying stuff and reselling out of their garage.
As has already been said, a record store has to have a LOT more than vinyl. It has to have multiple reasons for people to go in.
(I’m now thinking of the Vinyl Cafe, run by Dave and Morley. Just don’t ask Dave to cook you a turkey)
Ship them to the OP 
My last time was roughly the same timeline, maybe a year later. But they did also sell some new/used DVDs (I was there to try to offload some of those). That local store opened in 1981…and closed last month.
Donate them to a local charity shop. Many of these shops have sections for vinyl and cds’ and I often see folks looking through these stacks.
If you have 70’s and 80’s albums, they may be worth something Especially new wave. Especially original releases.
90’s rap and hip hop? Have value, depending on the artist
Classical? Not worth taking in, donate.
Nana Mouskouri? Donate (every charity shop near me has dozens of titles)
Roger Whittakar? Donate.
Before just chucking them, do a quick search on the Discogs site. Be sure to search by label and catalog number (often found on the spine)
There is a record store in Detroit where you can have your own records pressed which can include old, out-of-print recordings. More, it is possible to choose colors and design of your record. It is called Third Man Pressing and was opened by Jack White (White Stripes).
I am sure this is waaaay beyond what the OP envisions (there is a lot of expensive equipment and labor to make it happen) but it is a cool way to get that vintage vinyl album you always wanted (assuming you can get the recording to do it).
I can’t edit last post:
I should add I am not sure how the record sleeve is done or if you can print album notes (I suspect that is not possible for many reasons) so there can still be value in that vintage original album with all the things it came with.
Hey everyone – thanks for the great conversation (while I was offline) and the many, many great tips.
I even appreciate the doomsayers (you know who you are) who worry that I’m committing economic suicide. I get it. I’m naive, and full of dreams, and have never done this before. And most new businesses fail.
But please give me some credit. I’m talking with a lot of people who are and have been in this business. These stores can be run successfully, and I’m hoping to learn how. Starting this thread is another attempt to broaden my intake of information, but far from my only channel.
And I also understand I should be prepared to lose money. So far my total investment is about $50 – lunch and beers from a few meetings. 
Yes, I’ve having fun pursuing this hobby. But if it looks like a longshot for this investment to work, I’m not gonna do it. Okay?
IANAL, but it feels like there would be some copyright issues involved. For the music, as well, I assume. Although if the shop exists, White has presumably worked those out.
There’s only one indication for a small business not being open during posted hours, and that’s illness or a family emergency, and they should post a sign on the door indicating so.
Bob, the guy I saw at the grocery store, knows the music and the market inside and out, and one of his partners is the electronics expert.
I think Bob and Laura, the woman who handles the vintage clothing, know each other from somewhere else, and why not share space when there’s a space that’s too big for one business, but just the right size and location for both?
Based on the antique malls and flea markets Ms. SMV and I visit, the Venn diagrams of “buyers of vinyl records” and “buyers of vintage clothing” have a lot of overlap.
Without actually knowing the people involved, I assumed it was something like that – multiple friends utilizing the space because it works for everyone versus the guy starting a record store and then spinning off into vintage electronics and clothing to stay afloat.
There’s a gaming store (board games, D&D stuff, etc) with a bird feeding section. Why? 'Cause the guy’s wife wanted to sell bird feeding stuff 'cause she likes birds. It’s not an indictment on how well they do selling board games, they just had space she could use for her interest without starting a whole second bird feeding shop.
There’s at least one thread here on the Dope about unusual combinations of businesses that share a storefront.
Your post reminded me of that, and I just thought of the pharmacist whose first job out of school, ca. 1960, was at a store where the back end was the husband’s pharmacy business, and the front end was the wife’s pet care supply business. Our conversation included pay discrepancies back in the day, and she admitted that the owner did pay himself more than he paid her, but she didn’t mind because in addition to having extra responsibilities as the owner, he would do things she didn’t do, like come in at 3am to unload bird cages off the truck.
I can believe it, for both men and women!
When Bob’s kids were young, his wife wanted to be a SAHM and he supported her decision, so he got a “real” job that had health insurance and a stable paycheck, and did record fairs once or twice a month, and then when the kids were in school, he reopened the storefront and it’s done quite well.
This has been mentioned earlier, but it strikes me that you really want to put a lot of thought into the name of the store and your logo. Branded products (shirts, hoodies, coffee cups, etc.) could be a very helpful revenue stream, as well as providing advertising. Just take a look at the number of YouTube channels with recognizable merch. And one consideration for merch would also be whether or not you can come up with variations on the logo/store motto, witty comments about records/music, and so forth.
There’s nothing wrong with people dropping in because they either saw one of your t-shirts or simply wanted to buy one.
In his Australia travelogue In A Sunburned Country, Bill Bryson claimed he came across a pet store that sold porn in the back. He investigated, purely for journalistic purposes, of course (“and I hadn’t gotten anything for the kids yet, either.”)
Yes, yes and yes. My day job is in marketing, so this is naturally the part where I have the most ideas.