Many reports have been as quick as 2 days. I was quoted 5 days for ship time, but received a device back next day. Others have received a trade at the store. It seems like it's dependent of the store.
Accidental damage is not covered under warranty, so you could take it to any number of places. The repair itself is not trivial though, so you'd want someplace you can trust, and preferable is an official Apple authorized repair facility.
From past posts here and elsewere, it seems if Apple does it, the cost is somewhere around the $300 USD mark and typically takes a couple of days (assuming parts are available - replacement parts are not always readily available as most iPads "repaired" under warranty are actually replaced with factory refurbished units, and the broken item gets sent back to China for refurbishment if possible).
Other online places say the repair can be from $129 to $220-$250 depending on damage. iFixit has a guide to the process - http://www.ifixit.com/Guide/Installing-iPad-2-GSM-LCD/6161/1 and rates it as a "very difficult" repair.