Are you attending a performance or just going on the tour? The tours of the Semper Oper do not have a dress code but the performances are very swanky and if you aren't thrown out for not having a suit, you'll at least get the German version of the "stink-eye". You're going to one of the most glammed up Baroque opera houses in Europe so it is worth seeing. If you haven't been to the Albertuneum or the Frauenkirche down the street, you should do that too.

Cheap places to eat: Most of the places I ate at were just run of the mill Imbuses for Doner Kebaps. They were about 3-4 Euros. There are several in the old town shopping district just south of the Frauenkirche. Most of the cheaper sit-down restaurants to eat were, from my memory, in the Neustadt across the river. The places in historic Altstadt are expensive if you are on a budget. If you haven't used them before, the Let's Go series has good budget restaurant recommendations and they've yet to lead me to a bad meal.