For an apt. / hotel type place, try either Adina Apts. or the Residence Inn by Marriot near Eschenheimer Turm.
These are my top sites to see in Frankfurt.
Alt Stadt
Römer & Römerberg
Kaiserdom (St. Bartholomews)
Alte Oper
Städel Art Museum
Medieval Jewish Cemetery on Batton Strasse
Karmeliter Cloister
Klein Markt Halle
Eisener Steg Bridge
Jewish Holocaust Remembrance Wall
Palmengarten & Botanical Garden
Deutsche Ordens Kirche
Main Tower
Frankfurt Höchst, including Justinus Church
Eschenheimer Turm
Goethe Turm in the City Forest
Chinese Garden in Bethmann Park
St. Leonhard’s Church
Konstablerwache Farmers Market on Thur. & Sat.)
Schiller Market on Fridays
Bergerstrasse Market on Wed. and Sat.
Old Sachsenhausen
Towns or sites to see outside of Frankfurt - Hessen Park Open Air Museum, Saalburg Roman Fort, Büdingen, Limburg, Marburg, Mainz, Seligenstadt, Idstein.
Events in Sept. :
Frankfurt Rheingau Fest – 30.08-08.09
Bad Homburg Lantern Fest – 1-4.09
Frankfurt Harvest Fest – 21-23.09