I suggest saving up some more money and buying an Xbox

However, if you want some Ps2 suggestions anyway:
Kingdom Hearts - Most people love this game. I enjoyed it thoroughly. Its a bargain bin game now too. No reason not to own this thing.
God of War - If you like a 3rd person combat game with a cool story (Think... Ninja Gaiden with more on story. I haven't actually played much of God of War, but I did play the Demo so much my PS2 no doubt wept. I just havent gotten around to picking it up yet)
Tom Clancy's Splinter Cell: Chaos Theory - No idea how this'd play on the PS2, but it's a mean machine on the Xbox. Granted, you'll be missing out on Co-Op and Versus mode due to no Xbox Live, which really really added major value to the game (Especially that co-op mode man, so neat). Single player IS fun however.
Theres alot of entertaining bargain bin games too to keep in mind.
Tony Hawk Pro Skater 4, Crazy Taxi, Ratchet and Clank. All semi-amusing and fun games. Nothing "epic" in any of those, but if you can get them for a couple bucks they'll most defenitely keep you entertained (especially Tony Hawk and Ratchet and Clank, something about those games were unreasonably time consuming). My fiancee loves Crazy Taxi for whatever reason, so I included that
