Beer halls and pork knuckles aren't typical Saxon. Saxons have a sweet tooth and like their "coffee and cake" in the afternoon. In the small old town I can recommend the Grand Cafe und Restaurant im Coselpalais, which is right beside the Frauenkirche, and a very small place called Dresdner Kaffeestübchen, where you must try a Eierschecke, the local specialty.
If you are looking for a restaurant with local cuisine try the Altmarktkeller, which offers the typical mix of Saxon, Thuringian and Bohemian/Czech dishes. IMHO a Soljanka is a must in Eastern Germany, apart from that try something with dumplings or Knödel/knedlik.
I don't think that you will have the time to see more than the obvious highlights. If you are into museums the ones in the old town can already keep you busy for two days, and even with limited interest I would recommend to see at least one of the museums, which are quite unique.
And if you are looking for something completely different you can do a short tour with a paddle steamer:
https://www.saechsische-dampfschiffahrt.de/wp-content/blogs.dir/1/files_mf/1445439165TarifePreise2016.pdf
The short "Stadttour zu Wasser" crosses several castles and end at Blasewitz, a posh suburb with beer gardens, wine villages, villas and so on, the longer "Schlösserfahrt" goes a little further and ends at Pillnitz castle, a Chinoiserie palace with a wonderful garden.