Unexpected!!!!!

Most hotels near an airport will accept one night stays. Try googling "hotels at venice airport" and you should be able to find something. I would imagine that the big chains are near airport but can't help you with price.

What is the date that you need to overnight near the airport?

Arrive on the 20th in the evening and leave on the 21 in the evening.

Hotel Titian Inn Venice Airport Via Orlanda, 240/244 30173 Venezia - Tessera (VE) Tel. +39.041.5416846
Fax +39.041.5416843 You can do one night her for somewhere between 80 and 100 euros

We have stayed at the Titian inn before and it was fine. But with that much time and a late departure, I would suggest staying in Venice proper. Have a nice dinner stroll the streets. You can have lunch the next day and get out to the airport pretty easily and cheaply via public transport.

Ron's idea is great, particulary if Venice was not part of your itinerary, but it would be quite a challenge to find anything in Venice proper for less than $200 per night. Maybe with alot of internet searching you might. If the money is not a concern, go for it, particularly if this is your only chance to experience Venice. If you are counting your pennies at this point, stay outside of Venice (airport, mestre) and if your hotel is near public transport, either train or bus, you can get into Venice for anywhere from 1-10 euro, depending on the type of transport. Those prices are base on my research when I considered booking a B&B in the Mestre area, which was across the causeway that connects the mainland to the train station.

www.venere.com is showing availability in the 80 to 120 euro range for your date.