For vintage video games, you can find mom and pop stores all over the place. Some of them even have some basic repair services. Do a search, see what you find locally.

For vintage computers, I've never seen a dedicated store to this kind of thing that is still around. It's too niche of a market, with product that wont move fast enough to dedicate retail space to it.

Be sure to do a little research before heading to the mom and pop. These days most of these places are over priced or priced at the high end of what the market will bear because they are selling nostalgia. For example, a store in my city will often run out people that browse, and will adjust prices based on feeling or what the highest asking price on ebay for a mint version is on ebay plus markup.

Another issue, at least in my area, is the people that are out to flip vintage equipment. These people make their money off of scooping up anything at a bargain price and reselling it for more. One guy locally picks up every CRT TV and Monitor he can get his hands on that is in decent working order. He wipes them down, "services" them, and resells them online for 5 or 6 times what he paid. Other people in town do the same for vintage video games.