I fully agree with Chani. You try to see too much. I don't know from where you're leaving Germany, but if you travel slower you see much more of the country (not just train stations) and get a much better feel for the country. To give you an idea what you're missing:
The city offers enough world-class museums for at least 3 full days (Museum Island, DHM, Kulturforum). You should do at least one day trip to Potsdam, which is wonderful in late May. Potsdam offers not just Sanssouci, which already requires a full day if you want to see the whole park, but several other royal parks. Like Babelsberg (pic), the New Garden with Cecilienhof (pic), Peacock Island (pic) or structures like the Bevedere (pic) for example. Since you like nature you could also do a day trip to Spreewald, where the Spree meanders in thousands of small waterways through meadows and forests (many pics). Or visit Luthers house and many other places related to the Protestant Reformation in Wittenberg (pic of town square). or see Schwerin, one of the most beautiful German cities, with the Neuschwanstein of the north (pic of the castle).
If you spend only one day in Dresden you most probably visit one or two museums and see the old town. That's good, but you miss the best part, because the inner city was completely destroyed in WW2 and only partly rebuilt, while everything in the surroundings survived. You don't do a day trip with the fleet of nostalgic paddle steamers (pic) to sights nearby, like Pillnitz castle (pic), Saxon Switzerland (many pics) or Königstein fortress (pic). You also miss the beautiful towns in the surroundings, like Meißen, Freiberg (gallery of both towns), Bautzen or Görlitz (gallery, which includes both towns). Dresden is surrounded by vineyards (pic) with cozy villages (pic) and castles (pic), and two hours away is Germanys Christmas country, where you can shop all year (pic of shop).
While Rick Steves 6 days are too much, 2 days are definitely not enough. Stay 3 days to see the city, and add one or two days for day trips to Kutna Hora or Karlstejn.