check out some thrice, there like my favorite band, or if you want some other cool stuff listen to the living end, there kinda jazzy punk, that borders ska which is good. plus there often called the australian greenday. so yeah check them out.
+1 to the living end. They have a nice variety of music, so you'll find something you like.
OLD Incubus - the best music ever. Nice funky rock/metal. I suggest the album SCIENCE but Fungus Amongus has some great tracks too
Fav tracks: Speak Free, Take me to your leader, Deep Inside
The Police - obviously softer kind of rock, but Summers and Copeland create some really cool grooves if you look into them.
Fav tracks: DedododoDedadada, Don't stand so close to me
The Endless Sporadic - Not signed to a label yet, but oh my fucking god, they make some great shit.
Fav tracks: Sun of Pearl, Impulse
The deftones - I'm not a huge fan, but there are a few tracks on White Pony that I listen to daily; they can be really creative and trippy when they want to be.
Fav track: Change (in the house of flies)
Primus - Les Claypool is a bass god. This is as experimental and creative as it gets. Another band with a wide variety of music.
Fav tracks: Laquer Head, Jerry was a racecar driver, My name is mud