Overnight in Dresden OR Be Spontaneous For A Day Between Dresden and Bacharach

What are your interests?
The reconstructed centre of the city is very small and doesn't need more than a few hours, but the museums are world-class and some of them are very unique (Green Vaults, Turkish Chamber, Armory, Cabinet of Mathematical and Physical Instruments or Porcelain Collection), and if your into museums plan as much time as possible. The opera is also a great experience.
If you prefer to see "Old Europe", i.e. old cute towns and/or castles spend more time on the road.

I think Martin has summed it up accurately. I thought the Historical Green Vault (timed ticket required, but the regular Green Vault is also good) was an extremely impressive collection of beautiful objects. I'd see it again in a heartbeat, but you may be museumed out after Berlin. However, I didn't see anything in Berlin equivalent to the HGV.

I thought Dresden was particularly beautiful after dark. I had two nights there, one full day. Here are my photos.

The direct driving route along A4 and A5 between Dresden and Bacharach offers you several interesting options for stop-overs... but driving it all in one day doesn't give you time to do much other than drive and stop for meals.

On a slower paced trip, I would say Meissen, Altenburg, Weimar, Erfurt, Gotha, Eisenach, Bad Hersfeld, Alsfeld, Marburg (university town, daughter might enjoy), Wetzlar and Limburg all are worth at least an hour or two stop. If don't leave Dresden until after lunch, you won't have time to see anything along the way.

Since Google Maps shows the trip as 5:30, it could easily take 7 hours in real life. That leaves little time for getting off the highway, parking in a garage, and seeing more than one town, and certainly not a big place like Weimar (! not as big as Frankfurt). One could argue that you don't need to see both the old towns on the Rhine and also Erfurt (which I liked very much.) But you wouldn't have time, for example, for the fine EGAPark gardens in Erfurt, nor for Buchenwald near Weimar. Another option is Quedlinburg, which looks much older than some of the Rhine towns. But again, it's way off the highway.

As a practical matter, I would try to get halfway to Bacharach before spending the night, so I didn't have all that driving at once. You would also have plenty of traffic around Frankfurt.

We spent two nights in Dresden, including a boat ride on the Elbe and advance reservations for the Green Vault. It is difficult to overstate how much important art there is in Dresden. For example, there are 58 paintings just by the two Cranachs. We didn't have time to see the Zeiss optical museum in Jena. We actually did more driving during three nights in Weimar, including the day in Erfurt. This area is associated with the Bach family, if you have any interest in music.

Since Google Maps shows the trip as 5:30, it could easily take 7 hours in real life

Even 7 hours seems like an underestimate to me.

A road trip could look like this:
1. arrive 11:00, get your rental car (behind train station), leave Dresden ~11:30
2. drive to Kriebstein castle (1h), visit castle (2h), leave around 15:00
3. drive either to Erfurt or Weimar (1:30 to 2h)
4. explore the town in the afternoon and evening and spend the night there
5. continue to explore Erfurt/Weimar on the next day or, if you not that interested in Goethe or Schiller, leave Weimar in the morning
6. if you left Weimar in the morning visit Wartburg castle
7. leave Erfurt or Wartburg castle in the afternoon to cross Frankfurt after the rush-hour and arrive at Bacharach in the evening.

Since Google Maps shows the trip as 5:30, it could easily take 7 hours in real life.

7 hours would be some serious traffic! Google maps takes traffic into account and current predicts 4:50 trip even with an extra hour of delays on the A4.

I've driven this route several times and Erfurt is a good spot to split the drive up. You could arrive in Dresden, see the sights and the city at night then the next morning drive to Erfurt for lunch and sightseeing for a few hours before continuing on the Bacharach.

Erfurt is an underestimated gem for most tourists.

DJ

DJ, what can I say? I've rented cars in multiple countries, and I've always found GPS and computer estimates to be way low. Many posts here describe Los Angeles like conditions on major German highways (probably not as bad in the former East.) And after all, the OP described it as a leisurely trip, not a high-efficiency dash. We saw a billboard for the regional garden show while driving back to Weimar from Quedlinburg, but couldn't take time to stop.