Frankfurt Flughafen is the right choice for what you have described.
There is a tube stop in the airport where you can take the “S-Bahn” to Frankfurt Hauptbahnhof. It leaves every 15 minutes between 0500 and 2330 and it’s a 15 minute ride.
From Frankfurt Hauptbahnhof it’s a 10 minute walk along the river to the Römer Platz (the cultural center of gravity) where there are riverboats waiting to take you on an excursion up the Rhine river to scenic locales like Rüdesheim am Rhein (wine tasting in season).
The same “S-Bahn” leaving from the airport can also take you west to Mainz and Wiesbaden.
FRA is about 15 km from the center of Frankfurt. HHN is about 125 km away. FRA is also closer to Mainz than HHN is.
Credit:stackoverflow.com‘