Frankfurt has some world class museums, for a city it's size, it is quite impressive. Most are located next to each other along the Main River. More info > http://www.frankfurt.de/sixcms/detail.php?id=5021811

The city is very compact, so it is easy to walk around to see all the sights. 12/26 will be a holiday, shops will be closed that day, but bars/restaurants are open.

I would highly recommend to cross the river to Sachsenhausen and experience one of the local Appelwinetaverns. Fichtekränzi(opens at 5pm), Struwwelpeter, Dauth Schneider, Atschel, Kanonensteppel, Germania are some of my favorites. Some of these are over over 100+years old and offer great/high quality local food.

As for daytrips, Rüdesheim is a favorite along the Rhein River with all the castles and only a 40 min trip by train. Not sure how the schedule is for River cruises, just contact the kd line > https://www.k-d.com/

Frankfurt is surrounded by beautiful villages, we even have a House Mountain called Feldberg that you can reach via subway and a busride up the mountain(maybe there will be snow, right now it is to warm, but who knows how the weather will be in a couple of weeks)

Michelstadt is one of my favorites, although a good hour+ by train away, it is worth for a daytrip. Closer are Bad Homburg, Mainz, Wiesbaden, all worth a daytrip and easy to be reached via S-Bahn aka commuter train.(They run frequently aka every 20/30 min)

As for Hotels, as mentioned above, Frankfurt is compact, so the area does not really matter. Most hostels are around the main railwaystation, which also hosts the red light district, although not dangerous, some people are just not comfortable with it. City Centre would be fine, Sachsenhausen as well.Maybe check Hotel Maingau http://maingau.de/en/hotel/.html . It is located in the artsy district, close to Old Sachsenhausen and the Applewinetaverns, yet easy to walk over the river to Downtown Frankfurt.

Hope that helped a little