I'm not trying to discourage you from going to Frankfurt, but there is an alternative if you want to take it. When I have an early flight out of FRA, I always stay in Mainz, near the Bahnhof. There are several reasonably priced hotels right across the Bahnhofsplatz from the station. I stayed at Hotel Königshof in 2008, and it was nice. A double room is 82€ ($89) for your date. That rate includes a great breakfast buffet; many hotels in the area charge an additonal $25 or more for breakfast. Not just German breakfast items; one table at the buffet had a selection of American breakfast items (bacon, eggs, etc).
When I was at Königshof in 2008, I booked online but was not asked for a credit card prepayment. I could have cancelled at any time. So compare this price to the higher, fully-refundable room rate at other hotels.
I haven't stayed at Hotel Hammer, next door, but it also looks nice.
The area around the Bahnhof is a short walk (¾ km) from the old town of Mainz, with several museums, including the Gutenberg Museum, the 800 y.o. Cathedral, and the Rhein river.
When I was there in 2008, I thought the restaurant pickings were a little slim. There is an Italian restaurant next door to Könighof and an Asian one on the next block, but I wanted German food and couldn't find a German restaurant. According to Google Maps, there are more selctions there now.
There is an S-Bahn from Mainz Hbf to the airport every half hour. It takes 26 minutes (compared to 10 minutes every 15 minutes from the Frankfurt Hbf), but when I was in Frankfurt I didn't find any what-I-would-call-decent hotel as close to the Bahnhof as in Mainz. From both places, the S-Bahn comes into the Regionalbahnhof, under the building across the access road from Terminal 1. Come up the stairs from the station, and you are in Terminal 1.
Termainal 1 services primarily Lufthansa and Star Alliance airlines. A lot of other airlines use Terminal 2. You can get from Terminal 1 to Terminal 2 by using the Sky Line people mover between the upper floors of both terminals.