7 days in Germany - suggestions that allow a stop in Dresden and Werdau

By car or by rail? 7 days is more than enough for what you have proposed, but specific suggestions would depend on your method of transporation.

We will start with a week in Prague- my husband is there for work. We are then going to go to Germany and rent a car for the remainder which will actually be 6 days. We will be leaving to return home from Munich.

Well, you could spend 6 days in Dresden and one in Werdau for example. In Dresden you could see the old town, spend at least two days in museums like the Green Vaults, the Old Masters or the Armory, do day trips with the fleet of nostalgic paddle steamers to sights in the surrounding like Meissen, Pirna or Königstein fortress, you could visit the vineyards and wine villages in Radebeul, or take the steam train to Moritzburg castle, you could hike in Saxon Switzerland or take the train to perfectly preserved towns like Bautzen, Görlitz (where Grand Budapest Hotel was filmed) and Freiberg, or you could see Seiffen, a village with nothing but Christmas shops.
Werdau itself isn't that interesting, but it's close to Zwickau, which offers a preserved old town and the August Horch museum.
If you don't want to spend so many days in Dresden I recommend a few days in Erfurt, which offers one of the biggest and best preserved old towns of Germany. From there you could do day trips to Weimar and Wartburg castle.

Thank you so much . We are hoping to see more than Dresden though. We were wanting to start there. Any recommendations of a nice moderately priced place to stay in Dresden? Then we were wanting to do some additional stops ( to include Werdau for a quick stop to say hi to extended family) and eventually end up in Munich. The Bavarian part of Germany - Tirol - seems like it might be nice too. Is that feasible in 6-7 days?

If you wanted to include the Bavarian/Tyrolian Alps, I would head there immediately after Werdau and give yourself a few days, depending on how much of Munich you wanted to see. Enjoyment of few other areas of Europe are so dependent on good whether as the Alps. Therefore, you should allott a buffer of at least 2-3 days. Head up into the moutains as soon as the weather clears, and on cloudy or rainy days, use your time for daytrips to places like Füssen or Chiemsee.

If the Alps aren't so important, you could choose to stay in Nürnberg before heading to Munich.

In Dresden, I stayed at Hotel Steinberger der Saxe, right on Neumarkt. It wasn't that cheap, but was a decent value for the quality, and you can't beat the location or the view.

We spent an enjoyable day in Meissen followed by two in Dresden and felt we covered the highlights. After your time in Prague and a few days in Dresden, you may want to spend the rest of your trip exploring Munich (unless you've already been there).