We spent a week in an AirBnb Sankt Goar apt last Oct - it was a great apt with a direct view of the Rhine River in a small village with some nice restaurants, a bakery, and a butcher. However, the grocery store was in the next town. We also spent 3 nights in Frankfurt in late Nov before flying home - I was not impressed with their Xmas market or the town. It is a large city, where the small German villages and towns are much more charming. So I would suggest that you allocate more days to the Rhine and Mosselle River areas then to Frankfurt - JMHO. But Frankfurt does have Museum row, if that is your interest.
Many repeat visitors to the area suggest using the trains instead of renting a car. We are going to use the trains, but in the end, my girlfriend who had lived in Germany 30 yrs ago, joined us and we rented a car.
If you read the travel forum on Tripadvisor for the area, you will get lots of good suggestions on what to do and detailed info on how and which trains to take from Frankfurt. I was a big worried about using public transportation in Frankfurt, but we did take it from the Main Train station downtown to the airport and it was simple - no problem whatsoever. And cheaper and faster than a taxi per Tripadvisor folks. Of course, we purposely stated at an apt right next to the Train station.