There's not really that many decent game shops in Leeds city centre, bar the two GAMEs, CEX and Gamestation, plus HMV have a decent selection. You can get decent stuff in Arcadia if you're lucky, plus there are plenty of charity shops (most of them opposite the bus stops near the Corn Exchange, though there is a good new British Heart Foundation in the back of the Merrion Centre). There is a Grainger Games in the Merrion Centre, which is pretty decent, plus it's worth checking the outdoor market on Monday, Thursday and Saturday because a fair few of the stalls sell second hand and new games.
A few more decent places to have a pint:
The Wardrobe (if you like jazz n' stuff, go here, one of my faves, it's bang next to BBC Leeds)
The HiFi Club (go on Sunday afternoons for the 'Sunday Roast', live jazz ahoy)
The Calls Landing (a riverside bar, not as cheap as The Angel(!), some think it's a bit poncey but I like it, plus they serve Sagres in pints)
The Grove (quite rough/knockabout in feel but famed for its live music, apparently Mark Knopfler drinks there when he's in Leeds, cool place)
And then there's the Fab Café up at the top of the Merrion Centre, which is basically a retro movie-themed bar with loads of movie memorabilia dotted about, I haven't been in for ages but the last time I went in they had a stand-up Sega Star Wars Arcade cab, plus table footy. It's a bit scuzzy and run-down but still has a nicely nerdy atmos. Yeah, you could go into Grainger Games, have a browse in the BHF chazza shop then pop in there for a pint.