3 days for Frankfurt is plenty. The city is quite compact, and there are few (if any) world class sights.

I would suggest spending 1 day in Frankfurt, and doing 2 day trips.

In Frankfurt, take a walk along the river Main. Visit the Dom cathedral and the Paulskirche church. If you are at all into art, visit the Städel Museum - very nice collection ranging from medieval to contemporary art.

For day trips, the options mentioned by the posters above make sense. Most of these are easily doable by train, but some are more convenient with a rental car (not sure if you are open to that).

My suggestions would be:

Visit the Rheingau wine region. Go to Eltville. Visit the castle there. Have lunch at a winery (for example, Schloss Johannisberg, or Schloss Vollrads) with a view of the river Rhine. Take a walk through the vineyards. This trip requires a car. It can be easily combined with Wiesbaden.

Visit Cologne. I agree the city is not extremely pretty, but there are a few interesting things to see. There is a high-speed train that only takes 1 hour 10 minutes, so that should be an easy day trip. In Cologne, visit the cathedral. There is a good choice of excellent museums (Ludwig Collection - modern art, Wallraff Richartz museum - medieval art; there is also an archaelogical museum with mainly Roman artefacts).

Hotels in Frankfurt are not that remarkable. Villa Kennedy, Jumeirah, and Hessischer Hof, as mentioned above, typically come up as the best options. If you are lucky, they are bookable for EUR 200.

An alternative would be to stay in the suburbs, either Kronberg (Schlosshotel Kronberg), or Königstein (Villa Rothschild, Kempinski Falkenstein). These are nicely located historical hotels in leafy small towns. I prefer the two latter options. Kempinski Falkenstein has a very nice of the Frankfurt skyline from their terrace/park. Would only choose these hotels though if you are happy renting a car or spending significantly on taxis - they are about 30 minutes outside Frankfurt.