I would not recommend visiting Rüdesheim or Assmanshausen, i think these towns are touristic rip offs. And the area around the "Alte Oper" is not exactly the old town which doesn't exist anymore (burnt down in an raid in WWII). The bars and restaurants in this area are quite expensive, nevertheless ok for having a drink and for watching people watching people
My recommendations:
down to earth Pubs / Bars: Alt-Sachsenhausen - a lot of traditional restaurants, sports bars, bars, pubs, music pubs... a party area with people from Frankfurt / Germany / eyerywhere...
Berger Straße: Bars, restaurants, pubs, but different from Alt - Sachsenhausen, a little bit more sophisticated, some very nice places!
Sightseeing: visit the tourist info located on a place called "Römer" (it's in the city center near the river), they will provide you with maps and infos in english. And the "Römer" is one of Frankfurt's attractions for sightseeing. Also worth visiting:
Frankfurt am Main This site is available in english, just click the flag on the homepage. Good for getting an impression how small Frankfurt is - the Maintower
MAIN TOWER This site is also available in english...
If you want to make a trip to places outside of Frankfurt i would recommend taking the train to Kronberg (S4, takes about 25 minutes) and having a nice walk through the park, the historic old town, visit the castle.
Have a nice trip to germany!
Hanx