Most of the neighborhoods that surround the inner city are turn of the century, so 1870-1910. Westend is the nicest one. Check out Hotel Beethoven, http://www.hotelbeethoven.de/about.htm , Hotel Goelz, Liebieg Hotel, or Villa Florentina. The city is easy to get around in whether by tram, bus, underground or just walking. If you want to be right in the city center, look at Hotel Mirimar, Spener Haus, or Adina Apts. The neighborhood by the train station is also very beautiful, with great architecture. If you can get into Hotel Nizza, you get the decor to match.
http://www.hotelnizza.de/eng/index.html
On the other side of the river is the neighborhood of Sachsenhausen. This hotel would be my choice then. http://hotel-am-berg-ffm.de/
For day trips, I would choose Büdingen which is only an hour away by train. Group day ticket from www.rmv.de would cost 26.70 € I believe. Book a private tour from the TI for the best experience. They aren't expensive and they take you into the massive walls and up onto the guard towers.
The Rhine is close by of course, but not sure where else you are going after Frankfurt. Bad Homburg and the Saalburg Roman fort, Heidelberg, Eltville and Eberbach Monastery, Idstein, Seligenstadt, Würzburg, or Kronberg. While in Frankfurt, head to the neighborhood of Höchst. Great farmers market from 7-13:00 on Tues. Fri. & Sat. Visit the Justinus church from 14:00-16:00 (closed on Mon. ) This church was built in 850. Frankfurt itself has enough to keep you busy for a couple of days too.