I secretly desire your console!

I question whether you'd like ICO. If I didn't like it, you probably wouldn't. Shadow of the Colossus is gold, though. SotC is fairly hard to compare to any game that I've played. You could possibly say it's a more violent form of puzzle game, in that the main challenge comes simply from trying to figure out how to get on the damn colossus in the first place. It's not some artsy fartsy crap, honestly (well it IS, but there's a hell of a game in there, too).

If you're not hung up on cartoony or cutesy themes, I'll second Klonoa 2 and the Sly Cooper games. Besides being excellent arguments for the proper use of cel shading, they're great platformers in their own rights. Hell, the Sly games may very well be the only true platformers left on the PS2; Jak and Daxter went all hybrid shooter in the second and third games, and the Spyro the Dragon games are all utter shit now.

Avoid FF10.

If you ever feel the urge to give RPGs one more shot, try out Wild Arms 3. The battle system is so-so, and pretty early on I found a huge exploit that let me blow through bosses effortlessly, but it's one of the few RPGs I've played in recent memory whose storyline didn't utterly insult my intelligence. I can't praise the game enough for making sense the entire way through.

I think Armored Core 2 is really cheap now, so it would be a low-risk try at the series. It's a total mecha nerd game; you assemble a robot from a huge list of parts, and go blasting through missions, tailoring your configuration as needed. It's pretty fun, but the controls and design have a fairly steep learning curve. It's not for everyone, but is definitely worth a try. If you decide you like it and go for the whole series, avoid Another Age like the plague. They can't give it away, and there's a damn good reason for it.

Lego Star Wars is simplistic, but way more fun than it ought to be. Once you've unlocked most of the characters, you can waste a lot of time just hanging around the bar area watching the Jedi and Sith have huge gang wars. Plus, Lego General Grievous.

How ya doing, buddy?

I didn't mention it, but I also endorse God of War. I was watching my brother playing it, and suggested to him, "No, don't just rip these guys in half, you don't get any red orbs that way." Any game where such a comment actually applies in context is officially awesome.

There's nowhere I can't reach.