I spent the last week or so in Dresden on holiday.
I stayed in the Motel One Palaisplatz, which is on the north bank of the river, the Neustadt side. I picked that rather than the Motel One Am Zwinger because it was cheaper, but decided while there that I'd made a good choice - the Zwinger one is on Postplatz which is a major traffic interchange and would probably be noisy even with good soundproofing.
It really was shocking to discover how the city was destroyed during WWII - many of the more famous buildings by the riverside, the Schloss and Opera House as well as the Frauenkirche, were only reconstructed relatively recently. Most of the city centre was reconstructed very uninterestingly by the DDR and more recent developers, there is more or less nothing of visitor interest between the Zwinger and the Hauptbahnhof. There are much more surviving old buildings in the Neustadt area which has a lot of good restaurants, even if some are very hipsterish.
I was very impressed with the art collections in the Zwinger, Albertinum and Schloss. The tourist office sells a pass for all the major museums in two days for 22 euros, which is good value for money but is a slightly short amount of time for the amount to see. Note that the same ticket is considerably more expensive, at 27.50 euros, if bought from one of the museums themselves. It does NOT cover the Historic Green Vault, but does cover the New Green Vault exhibition area.
The Green Vault collections range from the genuinely beautiful to incredibly kitsch items that make you lament how much better use the money could have been put to. I'm not Christian but I still feel that a table-top crucifix in which the cross stands in a huge pile of massive pearls is a bit tasteless. I didn't book a Historic Green Vault ticket in advance and had no problem getting one for the next timed slot.
I did a couple of tours out of Dresden - one to Moritzburg and one to Saxon Switzerland. I meant to go to Moritzburg by the steam railway from Radebeul, but got mixed up about train times and realised at the Neustadt station that I was too late to get to Radebeul in time for the morning steam train. Fortunately I then found that there was a bus leaving at around that time that went straight to Moritzburg, so I caught that, visited the palace, and got the steam train back from there to Radebeul. If your main interest is the palace, be aware that the bus calls right in front of it while Moritzburg railway station is quite a walk away.