The Wii does have better graphics than the GameCube (the GPU is 50% faster on the Wii, the CPU is also 300MHz or so faster), but the graphics aren't the real draw of the Wii (nonetheless, the graphics on quite a few Wii games are outstanding).
My favorite GameCube games:
-Super Smash Bros. Melee (a MUST HAVE game, especially for multplayer)
-Super Mario Sunshine (It was OK, but not as good as SM64)
-Mario Kart Double Dash (fun multiplayer racing game, but not as good as MKDS, which had more options)
-Sonic Adventure DX (I'm a Sonic fan, and I never had a Dreamcast. It's a fun adventure game)
-Sonic Adventure 2 Battle (port of SA2 from Dreamcast)
-Sonic Mega Collection (all the old Sega Genesis Sonic games on one disc)
-Luigi's Mansion (fun adventure/survival game with a Mario twist)
I also have an SD Media Launcher by Datel. It lets you boot homebrew games on your console. I use it to play SNES, GB, Genesis, etc games on the GameCube as well as copy memory card saves to and from the PC.