I know I've quit STS games a long time ago because of busy life (Even busier now). But still sometimes I need to play games to relax. I have these criteria of the games I am gonna play. I need advice about which games meet the criteria.

Must (All of the criteria in this category must be met)
1. Game Center achievements
2. Achievements not lost (I play the game offline, and I still can upload my achievements to game center whenever I connect to the internet. Like fruit ninja.)
3. Playable offline (At least some parts of it can be played without connecting to the internet. If I don't need this, STS games will be my choice of games.)

Want(Getting these criteria would be good. But without them is ok)
1. Visible achievements (Able to track my achievements and see which achievements I have)
2. Full feature offline
3. Free

I would bump this thread until Mid-September to get lots of info. Thanks guys.