I was in a similar situation back with my old Altima. Was just about to sell it when one rear tire was showing steel. Didn't want to spend money on a tire for someone else, so I went to a used tire shop in the barrio of Pasadena. Pretty sure the dude put on cock fights, or at least raised the fighters because there were a bunch of roosters in the back in their own little enclosure houses. Also pretty sure old Rubio had a hell of a bender the night before. there were 24 oz Dos Equis cans all over the place.
Rubio had a goodyear in my size and installed it for like $30. Off I went, happy with myself for saving cash. Well, next day the car starts shimmying real bad again. I figure it must be the alignment, so I take it to a reputable alignment shop. Not convinced it is the alignment, I opt for just the $25 diagnostic rather than the full alignment. As soon as they get it up on the lift we see the problem. The other rear tire was completely separating, but only from the inside. Looked fine from the outside. Back to Rubios.
This time there were slightly fewer beer cans and Rubio didn't have a matching Goodyear to the one he previously sold me. He had some off brand, but at this point I was fine with whatever. Pay my $30 and haul ass down the road.
On the way home from work the car starts really rolling rough about 55mph. It was fine up til 55, then it got really bad. Did a little homework on it and it turns out old Rubio didn't balance the tires when he installed them. Back to Rubios.
This time he had his now normal amount of beer cans. He balanced both tires/wheels at no additional charge and I sold the altima a week or so later.
TLDR - used shops are fine to get you through, just watch them, ask questions and bring cash. If you are keeping the ride for any length of time, pay the money and get it done right with a good tire.