Nuremberg and Frankfurt Germany

Nuremberg is very charming and you can get a good feel for the city by just walking, since most of the major sites are within the Altstad. Take a map (or use your phone's map) and head towards the city center. If you just start walking, you will come across Lorenzkirche, an ornate huge old church that was once Catholic but is now evangelical Lutheran. Much of the church was bombed during World War II, but they restored it to its original grandeur.

There is also the Holy Ghost hospital (Heilig-Geist-Spital), which sits on the river. It was built in the 14th century to care for the sick, disabled and elderly citizens of the town. Nearby is the Shöner Brunnen, which means “beautiful fountain”. Because the old slaughter houses and even the hospital dumped very unsanitary things into the river, the town build the fountain to provide clean drinking water to the square. And of course they made it as ornate and beautiful as possible.

I recommend visiting the toy museum, which is charming and has so many interesting items. I also loved the German National Museum, which houses some original Dürer and Rembrandt paintings, and several pieces by Tilman Riemenschneider, a gifted sculptor from the 15th and 16th century.

If you like Albrecht Durer, his house has been turned into a museum. I did not visit it but have heard good things about it. It sits near the top (north end) of the Aldstadt.

Near there is a street called Weissgerbergasse, which is lined with very colorful half-timbered buildings. Definitely make a point of walking through it - it's incredibly charming! Here's a photo of it. https://www.fotocommunity.de/photo/weissgerbergasse-in-nuernberg-abbe-foto/32963877

I'm assuming you know about the Documentation Center on the outskirts of town.

For restaurants, I highly recommend Literaturhaus, which is about a 4 minute walk from your hotel. It is on Luitpoldstraße near the Altstadt and open for breakfast, lunch and dinner. I ate several meals there, including breakfast and several dinners. The food was very good--lots of German entrees--and a large and varied menu. I really enjoyed eating here. https://www.restaurant-im-literaturhaus.de/

I especially liked that most of the patrons I saw in there were Germans. On several occasions there were groups of locals there for various events. One was a book club meeting and another one was a birthday party for a woman who was turning 90. The book club group was sitting near me and told me that they meet there regularly (we spoke in German, although the servers speak English).

I forgot to add that you can also visit Courtroom 600 if you are interested. It's a bit out of town but fairly easy to access via train. Check ahead for closings, though. https://museums.nuernberg.de/memorium-nuremberg-trials/visitor-information/hours

One more thing you might want to consider is the Documentation Center and Nazi Rally Grounds. With all the things you can do the picks are hard but whatever you chose you should have an educational day. By the way the last 5 trips out of Frankfurt we stayed at the Sheriden Hotel at the Airport. A little pricey, about 210.00 that is well worth it. (retired HFD)

I highly recommend the Documentation Center and Rally Grounds in Nuremberg if you are interested in WWII history. When we visited, the Center had a great deal of information on the propaganda of the Third Reich.

I would stay at the Frankfurt airport for your last night. There are several hotels there where you can just walk straight into the airport. We have stayed at the Sheraton and the Hilton Garden Inn, depending on the costs.

Frankfurt hotel recommendations depends on your budget, but I would look around the Hauptwache area and NOT stay at the airport. You have this beautiful, historic city to see!
Hilton City Center, Flemings, Moxy, Motel One, Ruby, Steigenberger Frankfurter Hof.

You might want to see some of the Holocaust Memorials in Frankfurt. The Jewish Remembrance Wall is especially well done. The Book Burning Memorial is located on the Römerberg. Stop into the Kaiserdom and see their photo of what the Alt Stadt looked like after it was bombed. A bit difficult to get to, but the university is located in the former IG Farben headquarters. They have info plaques on their walls that tell what this company did for the Nazis. The Norbert Wollheim Memorial is next to it. The Gestapo jail is near the Konstablerwache, but is only open on Sat. afternoons. Still, from the outside, it is chilling. Almost next to it is a memorial to Fritz Bauer, who initiated the Auschwitz Trials that were in Frankfurt and who was also responsible for getting Eichmann to trial.

Since you have an interest in WWII, check out a site named thirdreichruins.com. It has many pictures taken in Nuremberg and Frankfurt before, during, and after the war, and pictures of the same places taken in more recent times. Provides some interesting contrast

The best location to stay will depend entirely upon the time of your departure flight. Personally, I would opt for staying at the airport if there are available rooms. My preference is to avoid racing around on the morning of a departure flight. Considering your home destination, your day will be plenty long enough without adding another 15 or 20 minutes of transit to it. If you do want to see a bit of Frankfurt, you can check in to your hotel and then travel from the airport into the city. There are plenty of good places to eat. There are also some areas to avoid.
With all due respect to Ms. Jo, who does a great job of promoting Frankfurt and it's charms, Frankfurt is not likely to end up on your list of favorite places that you have been in Germany. I would not make an effort to allocate time to it.
I have some familiarity; I have been going there off and on since 1962 and once lived in the area. Throughout the 80's and 90's and early 2000's my company had offices there (Bad Vilbel). Without taking trips through the airport into consideration, from the 80's until I retired in 2015, I travelled and stayed there at least once and usually two or three times per year.
For my upcoming trip, I will do as I just recommended, stay at the airport and take the train in to the city for dinner the night before our return home. It is not the cheapest accommodation, but having done this many times, there is nothing else that is as convenient.