Gametime is now called "Sporty's". Jimmy Hodges owns it and to say that he's meticulous about keeping the equipment in outstanding condition would be an understatement. He was a pool player before he was a business owner and both the tables and house cues are well taken care of. The best was when he had Cue Time in Mauldin... that was a pool room. Sporty's is a club and while there is a separate section for the pool tables, it's still a club and it's loud. I still swing in there when I go home to visit but it's rare that I ever know anyone shooting pool. It's mostly dates & groups of friends (bangers).
I spend most of my time at the Palace, which is only a couple of miles from Sporty's so it's real easy to go back & forth if action does happen at one place and not the other. Mike, the owner of the Palace is there EVERY night and he's just a genuine, laid back, nice guy. It's just a stale beer & cigarette smelling pool room. There's always a little bit of action... sometimes cheap, sometimes fairly big, and there's a mixture of bangers, dates, groups of friends, etc.
Bailey's is "ok"... another date / group of friends hang out place. I know one of the bartenders there so I stop in once in awhile but not to shoot pool. That's also just a couple of miles down the road. They're all close enough that you could scope all three of them out, make your choice and be back to the pool room of your choice, shooting pool within 30 min.
Mr. T's... eh I don't want to say anything because I haven't been there since 1991 or 92. LOL, some places change a lot and others stay the same. I don't know if it's changed or not so I can't say for sure.... I just know that I didn't care for it back then.
The area of Greenville that you're going to be in could also help make the decision easier.... any idea where these family members live? Side of town, zip code, anything like that?
Greenville is pretty pool friendly. You should be able to find something to your liking.
have a safe trip & try to enjoy yourself.