I’ll suggest the following:
Banjo-Kazooie: Nuts & Bolts - really fun, not twitch-based. It may take you a couple hours to get into the vehicle-based gameplay, which consists almost entirely of constructing custom vehicles out of a variety of crazy parts in order to win challenges. Many, though by no means all, of the challenges are races, but there’s also darts, soccer, trash collecting, location defending, and pizza delivery. Coming up with an original way to beat each challenge is quite fun.
Lego Star Wars - mentioned above, it’s very approachable, as well as funny. The game doesn’t penalize you much for dying, which means you can plug away just about as long as you like.
Viva Piñata - sure, it’s made for kids, but it’s still fun. There are, what, three different games in the series now? Just about any of 'em should be great. The gameplay, in the first one at least, is basically about gardening: clear ground, plant stuff, make ponds, and hope that your little green space attracts piñatas from the wild, which you can then breed and sell and such. There’s a lot more to it, but that’s the very bare-bones version.
Finally, one recent hot one: Left 4 Dead. It is a first person shooter, which works against your stated interests, but hear me out. L4D is a zombie apocalypse survival game, made with online play in mind. As the survivors, you are one of a team of four normal people who have to make their way to a rescue point. What makes L4D so interesting, though, is that teamwork is absolutely crucial to success; if you go off on your own, you will get killed, and your team will fail. When your teammates fall, you will have to help them up to keep them going. And coolest of all, the game is run by a “Director”. See, the game is framed as if it were a movie, and the Director is an overseeing artificial intelligence that keeps things interesting. The Director is constantly making decisions about where the bad guys will appear, how many of them will show up, and how much of a break you get after you’re attacked, which means that the game is never the same twice. That keeps it from becoming boring or predictable.
Anyway, most or all of these should have downloadable demos available in the Xbox Live Marketplace (I’m certain that at least Banjo-Kazooie and Left 4 Dead do, as well as Lego Star Wars II). So, give 'em a try before you buy.
Oh, one more thing: there’s an SDMB gamertag on Xbox Live (aaa SDMB), where you can meet other folks from the board for some games. There’s also another community called “2old2play” that you might want to look into to meet some folks who, well, aren’t jackass 13-year-olds who just want to ruin your night.
