Hrm.... Avondale isn't too far from Glendale and our side of Phoenix. I dunno how close you are from where you're situated in Avondale, but you might check out
ManaWerx, which is in Phoenix but kinda close to the edge of Glendale. ManaWerx is a clean place, and has lots of space with long tables for gaming. The owner's apparently working on getting a small LAN space set up near the back, but nothin's there yet. They have a TV with some video games/systems that can be played for a few dollars an hour, or somesuch (I've often seen folks playing the Wii or the X-Box there, but I don't have spare cash to spend on video games lately).
I and a few others play D&D and D20 Modern/Future at ManaWerx most weeks, currently on Saturdays. The other players actually come from the opposite side of Phoenix and over in Chandler, so it's more of a drive for them then it is for me, but ManaWerx holds a lot of Magic tournaments and such. They've stocked some D&D and other RPG books (and can order more on request) since folks have started playing RPGs there for a while, but it's mostly an M:TG and other CCG store.
Some other folks play on some Thursdays or Saturdays, so I know there's another group of roleplayers that hang out there too, but the third group hasn't been around in a while. Still, you can find a few gamers there, and we'd welcome another player.
Besides ManaWerx, if you don't mind the further drive (from your side of town) to the Metrocenter Mall, you can check out Atomic Comics (actually just outside the mall, in one of the surrounding stores across the parking lot), and Game Nightz (inside the mall, down the stairs/escalators from the food court, across from the Waldenbooks).
Atomic Comics carries a ton of different stuff (aside from the obvious comic books, they have a sizeable RPG section and various anime/manga stuff, plus collectable card games and miscellany). They also run Magic: The Gathering tournaments and such; I don't know if any gaming groups meet there regularly or not, as I don't have a car myself to make the trip over there very often (whereas ManaWerx is fairly close to my house). It's a cluttered place and has the usual comic-book-store posters and whatnot strewn about, but not a sty.
Game Nightz carries various RPG, CCG, board game, miniatures wargame, and similar/related materials. They're a bit smaller than Atomic Comics and Manawerx in terms of space, but not tiny. Game Nightz runs some Warhammer tournaments or similar (I'm not sure exactly if it's Warhammer or just a similar game, since I've only been around when they were just setting up, or just putting the terrain pieces away), and I think they also run Magic tournaments but I'm not sure. Game Nightz is cleaner and less cluttered (just a bit cramped since it's stuck in a smaller mall-space), and seems a bit friendlier I think (again, I don't go out that way very often myself, so I have less experience with the place).
)! I love living here, and cannot imagine living anywhere else!
