First of all: If you only have a few hours for Dresden, you will only get a quick impression of the town, you will only visit a couple of the most famous sights, you will miss the nightlife and you will not be able to meet some people from Dresden or to get any deeper insights about what actually makes the town. If you travel this way you will mess up the buldings and cities you have seen after a while and you will take less home as you would with some more time to spend at the places.
But, what should you visit if you only have 3 hours in Dresden? Forget about the Neustadt or other real neighborhoods (where people actually life), you will only have time for the historical part of the town. Start at the Zwinger with the Crown Gate, its one of the landmarks of Dresden. On its northern part towards the river Elbe is the famous picture galerie the „Old Masters“. You will probably have to skip it, because a short visit there would cost you the three hours you have. Next to it you will see the square Theaterplatz with the Semper Opera to your left. You could visit the building on a guided tour, but again – no time unfortunately.
Just opposite you will see the castle of Dresden. It houses many very amazing exibitions, like the Green Vault or the just reopened Turkish Chamber. Next to it is the Taschenberg Palais, today used as a luxury hotel. You don’t have to move a lot, still on the theatre square you will find the catholic church Hofkirche which is worth a quick look inside. In front of the chuch is the square Schlossplatz and next to it you will find the Fürstenzug and the Brühlische Terasse, also know as the „balcony of Europe“. Watch the steamboats on the river Elbe departing and have a quick view on the big state buildings on the other side of the river. Don’t sit down and relax in the sun and enjoy the view and the atmosphere, remember, you have no time!
Later on the Brühlische Terasse you will pass by Albertinum where soon will be another picture galarie, the „New Masters“. You should definetely visit another landmark of Dresden, the well known Church Of Our Lady on the Neumarkt and also wander around this newly reshaped square. Have a look on the Johanneum, which houses today the transport-museum and don’t miss the view into the Stallhof. A few meters away you will find the Old Market Square, which is actually the old centre of Dresden. Pass the Kulturpalast and stop by the Kreuzkirche, another church but completely different compared to the kitschy Frauenkirche.
Thats it. No time for the baroque quarter around Königstrasse, no Golden Horseman, no Augustus bridge, no Elbe castles, no „Blue wonder“ bridge, no museums from inside, no National Park „Swiss Saxony“, no other sights in the surroundings. Hey but still, you can tell your friends you „have been“ in Dresden!