We are going to have a long enough layover in Frankfurt (20 hours) to have a short stay at a hotel and a little time to check out a site or place. Should we stay near the airport and travel to the site/place or stay near the site/place and travel to the airport? We arrive at 11:05 am and depart at 7:05 am the next day.

If you post on the Europe forum, and flag it for Germany, many more people will see your inquiry.

The answer is simple, really. Visit the site first then go back to a hotel at or near airport to sleep. If you spend the night near the site you’ll have to get up somewhere around 3am in order to get back to the airport in time to check-in and clear security in time for your 7am flight. If it were me, I’d stay at the Hilton that is right inside the airport near Terminal 1.

Moved to the Europe Forum

Are you expecting others to guess the "site" and give opinion on feasibility of visiting that "site" hoping the "site" we guessed is the same as your site? Also we don't know if you are arriving at 11:05 from other Schengen country as well as whether you need to retrieve your luggage after landing at FRA. Same for the 7:05 am departure: are you flying to a Schengen country with just a carry-on or are you flying to departure process time consuming destinations like the U.S. with a lot of checked luggage? Also how much you are willing to pay for the overnight stay has impact on how much time free time you can buy. Usually when one is further away from the airport, cheaper the stay but more time required to travel between the hotel and the airport.

I've stayed at the airport HGI several times; there is also an adjacent Hilton. Both are right above the train station and just across the street from the airport terminal. It is extremely handy for early morning flights!