Well, it was not easy to pick one the most favorite place up, but the winner is Leopold museum. I really like the permanent exhibition, which I can can go for 10 more times and still not get bored and also like to go for a special exhibitions which are always interesting.
And what you should try in Vienna? Definitely Wiener Schnitzel! it is not just a Schnitzel, it is something more and the taste is delicious and special in every possible way. there are many places and restaurants which offer it, however I recommend you to visit typical traditional Austrian restaurant.