Best places to eat and things to do in the castle district?

Well, lets start with defining "Best". Best as in Michelin Star? Best as in humble Hungarian? Best as in US burger?

Actually I am stalling. For me Buda is sort of special event destination and not part of our day to day in Budapest. We might go for a nice dinner or an event at the Castle or at the courtyard at the Hilton; and that's where FirstMed is located. So, I cant help you with day to day places, only special trip places. Check out:

Arany Kaviár Étterem
Halászbástya Étterem
Aranyhordó Étterem
Aranyszarvas Vendéglő

But since the Castle District is your favorite part of Budapest, you probably know a lot more about it than I do. Don't miss the Beer Festival at the Castle if you are there on the 11th.

Thanks for the feedback. I will check those places out. I am there on the 23-30th of July, so no beer festival. And ironically, I don't drink so it wouldn't matter-lol.

But you will be there at the time of the Formula 1 Hungarian Grand Prix. Unfortunately the Opera and the Operett and the Liszt Academy have already finished their season by then, but there are a few things going on at the Palace of Art https://www.mupa.hu/en/events/calendar/06/2015; and all of the standard tourist fare church concerts, musical boat tours and folk dancing programs will most likely still be running, as will the Friday night Klezmer shows at Spinoza's. July? You do realize it will be warm and there will be little effective air conditioning.

For desserts, Ruszwurm is a great cake shop in the Castle District, a short walk from St. Matthias'. Prices are reasonable and the quality is very high - exceeded my expectations, especially given the touristy locale.