I thought Myst was first-person?
If we're talking older games, I'd say the Quest for Glory series. PC, like King's Quest except not retarded or cruel.
If we're talking not-all-that-old games, I'd say Okami. Zelda clone in gameplay, much cooler presentation.
If we're talking newer games... no guns, no first-person, and no internet play... I've heard Machinarium is good? PC point-and-click adventure. You have a 360, but not a PS3, so it's a little hard to think of a game that isn't an FPS. >_>
Lost Odyssey, maybe? Wossitcalled... Infinite Undiscovery? I don't use my 360 nearly enough.
Thinking about it, download and play [
www.studiotrophis.com]
The White Chamber, if you haven't. It's not bad for a free game.