The only games I keep my 360 around for are Halo and Mass effect. Those two games represent the best of what 360 has to offer in terms of action games.
You already mentioned that you had Halo 3 but have you played through the first and second game? The first one was the best game of the whole franchise so that is really a must if you haven't played it already. And the second Halo is only for the story.
If you have even the slightest bit of a roleplayer in you, Mass effect 1-2 are games for you. ME 1 was a lot more like a roleplaying game than the second one so if you're not into roleplaying, ME 2 is still a good option for an action game (if you don't mind a hell of a lot of dialogue). Mass effect games represent the best of roleplaying games at the moment. Also ME franchise is a very good choice because of its replay value. Though you should play the first one through before jumping to the second one if you want to really max out the experience (since you can import your old character to the new game and your every choice counts and they might have severe consequences).
Hopefully I got you convinced of these games. They really are the elite of what 360 has to offer. If you still doubt that Mass effect could do the trick for you, go and check reviews from Metacritic for both games and visit the game websites.
