Way to go! I think it's a great idea. I've had a compost... pile for a while. It never bothered our neighbors. What would you do with the finished product? As long as it is well aerated, not meat, oil or dairy you shouldn't have to worry about smells. if you can get a few hand fulls of leaves or something to cover it you should be fine.
Try to Google apartment composting. Tons o' info.