Please don't bike on sidewalks. It's much less safe than the road (there's good reason it's illegal most places). :P
As a matter of personal preference, my quick checklist that I go over is:
- Does it fit comfortably? The seat can easily be raised or lowered, but the distance between the bars and the seat you'll be stuck with.
- Does everything look like it's in OK condition mechanically (shifters, breaks, headset, bottom bracket)
- Fenders, rack, lights, bottle holder, bar ends, etc. can all be added later when needed, but it makes things easier if the bike already comes with them.