Museum will be open on Sunday, but shops will be closed resulting in indeed less crowded city centres. Great, if you want to walk around without being disturbed by shoppers, take pictures without too much people and have a more relaxed day. Sunday Mornings are the best days in my opinion.
Public transportation is running on Sundays though on a slightly reduced frequency, so heading to Mainz is not a problem either.

Regarding your flights, the Sheraton, Marriott, Hilton and Hilton Garden Inn make more sens in this regard. Though I took the S-Bahn from Gateway Garden to Franfkurt Regionalbahnhof and walked over to FCT in August last year. If you loyalty to IHG is worth, it would be an option, though not the best one compared toe aforementioned four hotels.

Enjoy FCT.