Hotels around the airport are very expensive. As an option stay in Sachsenhausen which is the historic part of Frankfurt that is connected to the airport by direct bus #61. Ticket costs around $5. The Novum Hotel in Sachsenhausen is very inexpensive, perhaps around $55 per night, and convenient to everything and within one block of the river and bridges and night life. Just check their rates carefully as they will triple when there are conventions in town, but it is easy to plan your stay around those periods if your itinerary allows it.