Our second day in Dresden

Sorry to hear that you are skipping the museums , I would at least try to see the two green vaults . While both are terrific , the New Green Vault , with the work of the master jeweler , Dinglinger , is really impressive . Your second day seems overly ambitious for my taste , What I would suggest would be take the #6 or #12 tram to Schillerplatz in Blasewitz and walk across the Blue Wonder Bridge . Just the other side of the bridge you take the funicular up to Loschwitz , a beautiful villa area with varied architecture . Turn right out of the upper station and wander along Plattleite , up to Bautzner Landstrasse where you can board the #11 tram headed back to Neustadt .. Get off at Pulsnitzer Strasse and visit Molkerei Pfund . This a cheese shop with the most exquisite Majolika tile work I have ever seen . From there you can also wander The Neustadt before heading back into central Dresden .https://www.google.com/maps/place/Pulsnitzer+Stra%C3%9Fe/@51.0654729,13.759388,16.5z/data=!4m13!1m7!3m6!1s0x47a7465f01fd9de9:0x51ddf8280975d11c!2sChemnitz,+Germany!3b1!8m2!3d50.827845!4d12.9213697!3m4!1s0x4709cf3854c8378f:0xcdaec04a46be6392!8m2!3d51.0634004!4d13.7578963

It's a shame you're going to miss some of the absolutely incredible museums of Dresden. The Staatlichen Kunstsammlungen Dresden (Dresden State Art Collections) which, according to the institution's own statements, place it among the most important museums presently in existence.
We have relatives from Dresden (prior to WWII) when the city was one of the premier cultural and architectural centers of Europe.

Yeah, I'm starting to rethink things a bit, maybe do the Green Vaults on the first day, and the rest of our time that day just wandering. The other museum I'm looking into is the Albertinum, but I'd still like to visit these other parts of Dresden, as I'm interested in seeking out areas with beautiful architecture that are a little off the tourist beaten path.

With the Albertinum , you struck weak spot for me . This was one of my favorite museums anywhere . With an extensive collection of modern ( late nineteenth to early twentieth century ) art , a real highlight for me was the section of Neue Sachlichkeit painting . I'm back in Dresden for six days in September and can't wait .

Also, the Albertinum has some Casper David Friedrich paintings, one of my favorite painters.

The reconstructed old town is really small and doesn't need a whole day. You could easily squeeze in one or two museums, one in the morning, one in the afternoon, and still have time to see everything. Dresdens museums are really world-class, and some are unique, it would be a shame to miss them. My favorite is the strangely overlooked armory with the Turkish Chamber and the Electoral Wardrobe, but most people prefer the Green Vault(s), which is/are simply so unique that you have to see them. So, you could see one of the museums of the castle in the morning, and the Albertinum in the afternoon for example.

If you don't want to visit any museums you can see both the old town and the Neustadt area on the same day, which works better than Neustadt + suburbs, since you just have to cross the river. In this case see the old town in the morning and early afternoon, and the New Town in the afternoon and evening.

The suburbs around the Blue Wonder Bridge work great with Pillnitz castle. In the morning bus or tram (+ ferry) to the castle, early afternoon paddle steamer back to Blasewitz.

I preferred the Historic Green Vault, but all the museums mentioned here are very good. Alone among them (at least as of my 2015 visit), the Historic Green Vault requires a timed ticket. If yu want to see that one, I suggest going by the ticket counter when you arrive in the Altstadt to nail down that ticket. I didn't have to wait, but I snagged the last remaining ticket for the next entry period. I spent quite a long time in the HGV--definitely more than an hour; I love looking at beautiful objects.

Also as of 2015, the tourist office offered a walking tour I enjoyed.

The green vault is one of the best collections that I have seen.The Moritzburg Hunting Lodge of Augustus the Strong is worth visiting as well as the Albertinium.Meissen is up river from Dresden with their porcelain manufactory.Bautzen is near Gorlitz and you can see the culture of the Zorbs.There is also Saxon Switzerland accessible by car,train or boat,nice hiking area.Don,t forget the Fraunkirsche.
Mike

Another unique place in Dresden is Pfunds Market,it is a deli with amazing architecture and good sandwiches to boot and walk the neighborhood.
Mike