There are several hotels near the airport - check these!
They all have bus-shuttles!
Good booking site is:
www.hrs.com!
I would suggest:
- Steigenberger Airport
- InterCity Airport (has rooms for 66 Euro for tomorrow)
Or check Hotels in FRA-City (Near train-station)
It is only a 20 minutes ride by train!
Prices start at 35 Euro with breakfast!
I would not sleap at the airport!