We just moved from Sachsenhausen (area south of the river Main) to Bockenheim (area west of downtown)!!
My favorite places?
I really like the Palmengarten. I have been at least once in each of the four seasons, but I'd have to say it's the most fun in summer. See my off the beaten path section for more info.
I also frequent the Turmpalast (the only English Language theater in Frankfurt - the other theaters dub their movies into German). To get there, take the subway (lines U1, U2, or U3) to Eschenheimer Tor and take the Heiner Weg exit. You can't miss it. (see must see activities for more info)
Baerentreff is a great store on the Zeil that sells a German speciality - Gummi Bears - see my shopping tip below for directions!
I also like going for a draft cider at one of the many Irish pubs in Alt Sachsenhausen (get off at Lokalbahnhof and walk north to Affentorplatz).
I have put in a lot of restaurant tips - places that I like to go to eat. So check them out!