Of course, I'd specify Vice City. The 1st game was too damn grimy! I could cruise up and down the Miami-ish, art-deco, ocean drive for eternity, wind in my hair, ho behind my back, listening to the best music ever; 80's!
KoToR, Shenmue, Max Payne, Deus Ex, Matrix, Middle Earth, Tony Hawk 4, Gran Turismo 3, GTA3 or Vice City, man there are a bunch of others. Kid Icarus, Metroid, Metal Gear, F-Zero.. maybe Soul Calibur.
That's a tough question, I actually had to check my library because most gameworlds are not happy/fun. If death wasn't a concern, I'd try my hand at the Romance of the Three Kingdoms/Dynasty Warriors world. If death was a concern, I'd try my hand at Rez, Rush 2049, Jet Set Radio, or Magic Pengel.