There’s a bunch of cool, weird stuff from the 360 era worth checking out.
Banjo-Kazooie: Nuts & Bolts is a cool, weird vehicle building game that you can probably get very cheaply.
The Master Chief collection is great fun, especially with a buddy to play the campaigns with.
I hear Lost Odyssey was good, though I’ve never played it myself.
The XBLA had a treasure trove, too. The Banjo Kazooie and Banjo Tooie remakes are worth checking out.