OK so you don't like First Person Shooters, Role Playing Games, and Fighting Games. That cuts out a pretty big chunk of the PS2's library. But don't sweat it too much. The PS2's selection of games is so huge that even without those gener's there are still plenty of great games for you to play.
Since you like Guitar Hero so much I take it to mean that you are kind of into rhythem games. Frequency and Amplitude are some other great rhythem games that are amazing.
The ports of most of the Arcade Light Gun games are pretty awsome. Time Crisis 3 is going on sale next week at Game Stop for only $25 with 2 light gun controllers included. I'd definently recomend picking up a copy of that game.
If you want to try some great horror games I'd recomend trying out Resident Evil 4, Silent Hill 3, or Fatal Frame II. The Onimusha Games are a must play as well.
If you like platformers you can't go wrong with Psychonauts. Jak II and Jak III were also really great.
Also don't forget LEGO Star Wars. That game was awsome.
If you want to play some great Hack and Slash games go with either God of War, X-Men Legends II, or
Lord of the Rings: Return of the King.
As far as Racing Games go if you want some thing that is pure fun go with Burnout. If you want some games that are great but are a little more involved I'd recomend Need for Speed Underground 2 and Midnight Club 3.
That should be enough to get you started.