My husband and I are planning a short trip 4 days to southern Germany with my son. (He lives near London) We have spent time reading and watching Rick Steve's videos on the area. I think we will fly to Munich (a place my son wants to visit) then go to Berchtesgaden and Eagles Nest. Other places we may want to go are: Neuschwanstein Castle, Romantic Road, Zugspitze. We are thinking of spending 4 days in this area. Questions we have are: should we rent a car to go to some of these places, and if not, how should we travel from Munich? My husband thought we should stay in Munich the 3-4 nights 9as a base) but I thought maybe staying somewhere else part of the time might be nice. We are still deciding whether to go to western Germany (by the Rhine) after or taking the Eurostar to Paris for 2-3 days. We want to be gone a total of no more than 7 days. I forgot to mention we are leaving either May 17 or around 24th from London. We are in our late 60s.
Although I much prefer trains in Germany, I think a car would meet your needs better for the number of areas outside of Munich that you want to visit within 4 days. I would not stay in Munich if you want to drive. It is has traffic and parking issues. I would stay someplace south of town and catch a train into Munich when you want to visit it.
"...fly to Munich (a place my son wants to visit) then go to Berchtesgaden and Eagles Nest. Other places we may want to go are: Neuschwanstein Castle, Romantic Road, Zugspitze. We are thinking of spending 4 days in this area."
That's a very big meal on a very small 4-day plate. Seeing Munich itself could take a couple days.
"We are still deciding whether to go to western Germany (by the Rhine) after or taking the Eurostar to Paris for 2-3 days. We want to be gone a total of no more than 7 days."
This itinerary seems much more sensible to me. The Rhine/Mosel area isn't so spread out as your plan for Bavaria. Burg Eltz Castle, near the town of Cochem (roughly 4 hours from Paris by train) is one of 3 or 4 castles you might visit - after 8+ centuries, it and Marksburg Castle in Braubach are still intact (Neuschwanstein is "new construction" by comparison.)
With 4 days you can split your stay - 2 nights on each river? Or possibly base yourselves in a central town like Boppard for 4 nights and see some of both rivers from there. From the Rhine/Mosel region you can fly out of Frankfurt Hahn, Cologne, Düsseldorf, Luxembourg, or Frankfurt International, depending on flight prices and convenience to your choice of stop(s).
Southern Germany. I live in Germany and drive. With such a short visit driving might save you time. Munich is a big city, but if you narrow what you want to see it can be done in a day or two. I would recommend leaving Munich and overnight at your chosen destination; Berchtesgaden and Eagles Nest, Fussen Neuschwanstein Castle, Garmish Zugspitze. I think you need to decide one or two overnights outside Munich for southern Germany. Staying at other places gives you another view/perspective, a change of dinner, pub, breakfast etc. and a new place to visit explore. I think it is worth the hassle of moving.