Oh that's great. I travel to both quite a bit, at least pre pandemic. Vienna is an amazing city, Old World Europe with lots of cultural influences.
I have a lot of places to recommend, but go to the City Center for starters as there is plenty to see and experience.
Vienna S&Rs
Plachutta I recommend for traditional Viennese fare. Highly recommend getting tafelspitz, probably my favorite meal from any European country. It's located in the City Center/1st District within the inner ting of Vienna. The address at this location is:
Wollzeile 38
1010 Vienna
Comida restaurant for Latin-influenced fare. There is a nightclub that opens downstairs on the weekend. It is also located in the 1st District. The address is:
Stubenring 20, 1010 Wien
Take the Ubahn to Schönbrunn Palace. Located outside of Vienna.
Naschmarkt is good for lunch. Plenty if dining options.
Walk along Graben in the City Center for shopping. It's near Stephensdom/St Stephen Cathedral, which is generally the geometric center of Vienna.
Munich
Also has too many options to list. Every neighborhood has at least one biergarten where locals go to have beer and conversation. Due to its location near Northern Italy, Munich has the best Italian restaurants you can find outside of Italy. I'm not a fan of traditional German fare, so I usually dine at ethnic restaurants in the city.
English Gardens is a must see, even during winter as there will be Christmas markets.
For live music goto the Bayerischer Hof hotel
near Marienplatz and the Theatre District. The hotel is a high end hotel where most celebrities choose to stay.
Class of '91 (MEEN)