We have a 1 night layover at Frankfurt Airport and need reco's for a hotel.
We would like to see Frankfurt city (posssilby Mainz) and not pay a fortune in taxi cabs.
Any suggestions?

Either stay in Frankfurt or stay in Mainz, rather than staying at the airport. Your question is a bit vague, so it isn't really easy to give you an anwer. As in your other post, dates, budget, a couple, a family or just friends traveling.

The S-bahns are extremely easy to use, so need to take a cab.

I'm glad you responded Mainhattengirl. I have read your other responses.
We are arriving at the Airport @ 2pm and our plane leaves the following day at 10am. So we have just 1 night.
Preferably we would like to take a subway or train to a hotel at or near the airport, stash our luggage and then head back to the subway or train and enjoy Frankfurt, returning to the hotel for overnight. It's just the 2 of us, middled-aged (but spry and active) Americans.
It does not have to be a fancy hotel. Location and safety are important,so is a private bathroom/shower and cleanliness.
A chain hotel is just fine.
As I said I have read your responses to others and I would appreciate your thoughts on this.

Actually our plane arrives earlier, at 10:30 in the morning, which leaves more time in Frankfurt. While in Frankfurt we hope to visit the Jüdisches Museum, Alter Jüdischer Friedhof, and have dinner and walk around. We alternatively considered taking a walking tour if there is one that interests us that we can make in time.
If we stay in Frankfurt rather than at the airport, any hotel suggestions?

I did this (well, similar shall we say) just this past October. I stayed at the Hilton near the downtown in Frankfurt so you can locate it, but I am sure there are many options in the area to suit all price ranges (and it was an easy trip to and from the airport). Where we were was a very nice area of Frankfurt and as it was a Saturday, there was a market and celebrations going on in the pedestrian zone. Lots of food - restaurants, street vendors , etc.).

As for cleanliness, almost anything in Germany will be clean. I am amazed by just how clean everything was kept. I was in Germany for 6 nights and all the hotels and bathrooms in restaurants (even in small towns) were spotless.

Finally, I want to stress that there is no need to stay near the airport. I zipped in and out on the train (my Mrs and me, that is) and worst case, rent a taxi - but I don't think you'll need one. Enjoy.

As I mentioned in another post, have a look at these:

1. The Pure (design boutique close to main station and close to red light district, if that bothers you, and banks on hte other side)
http://www.the-pure.de/

2. 25 hours by Levis, close to The Pure, funky, unconventional, but very good and cheap.
http://www.25hours-hotels.com/frankf...ex.php?lang=en

3. Moevenpick, new, clean, anonymus, behind the fairgrounds and slightly isolated, but a short walk to the Westend and normally very good value
http://www.moevenpick-hotels.com/en/...y/overview.cfm

4. Hotel Liebig, very private small hotel in upscale Westend neighbourhood with renovated rooms in an older mansion. Close to nice little neighbourhood restaurants.
http://www.hotelliebig.de/

And with regards to proximity to Juedisches Museum, take a look at Roomers, which Mainhattangirl also suggested on another post, and which I don't have personal experience with, but which should be good.
http://www.roomers.eu/