Take a couple or 4 days in Vienna before adding the complexities of local travel on top of jet lag. 2 days is enough for Salzburg.
Your saying "Enjoy scenic/outdoor activities mixed in with some museum visits" leads me to strongly second the advice to rent a car.. Your St Wolfgang days are in the lake district of the Salzkammergut, where there are lots scenic drives & we have traveled all them multiple times. I have a note in my Michelin Green Guide on St Wolfgang-- "blah". There are so many better places to see in the Salzkammergut, don't waste a lot of time in a minor sight like St Wolfgang.
The Green Guide lists 5 recommended road trips in the Salzkammergut. In the lake district, I have added a note to recommended route #2, Bad Ischl to Gmunden-- "best drive". Don't know how to do it by bus, but 2 of the 3 recommended lake district tours (including the route to St Wolfgang) go thru Gmunden.
Best of the Salzkammergut: circle the Dachstein (Hallstatt, Gosausee)
Save Salzburg for bad weather. Explore the countryside scenery as long as you have good weather.
Consider Munch airport. Note: car rental prices in Munich city are cheaper than at the airport, but Munich is not a touristic hot spot.
You are very wise to not waste time in Munich & Salzburg. Your plans there are perfect.
Day 7: drive along the river: the Wachau to Krems, Maria Tafrl, & Melk. GO TO Maria Taferl BEFORE Melk Abby. Maria Tafrl is where Jacob Prandtauer practiced before he built Melk, and it shows. Do it this way and you will be blown away twice.
Prague deserves more time than Budapest.
Budapest: Most of Day 1 for Castle Hill (Buda). Then Pest. Day 2 for Pest.
Prague: Walk the streets. Then walk some more streets. Do not miss the view of the castle from the Old Town side of the Charles Bridge at night. Take in an opera at the theater where Mozart directed the premier of Cossi fan Tutti.
Walk the streets in Old Town. Walk the streets in Mala Strana, Walk the streets in the Jewish Quarter. Walk the streets in new town.
Celebrate anniversary with cake at Demel.
If I were spending 5 days in Vienna, my meal plan would be: Wienerschnitzl for 4 dinners, 1 backhendl dinner. 5 pastry shop breakfasts. 5 pastry shop lunches. 5 afternoon snacks at a pastry shop. And don't eat pastries, eat cake. An Austrian princess, Marie Antoinette knew what she was doing when she said, "let them eat cake".
Rent a car to go to Hallstatt. Much better way to see the sights (go thru Bad Ischl to Bad Ausee to the Dachstein to Hallstatt from the south). Most important, with a car, you can also visit the Gosausee, just over the mountain to the west of Hallstatt. Hallstatt is a quaint village on the shore of the modestly scenic Hallstattersee (...see means such and such lake in Austrian-- Lake Hallstatt is where Hallstatt h\town is located). There is no village at the Gosausee, but the Michelin Guide flat out states that the Gosausee "is the most impressive lake in Austria" Michelin is wrong. It is the most impressive Alpine lake in the world. You have never seen mountain scenery if you have not seen the setting of the Gosausee. So here is something for you to think about. You have booked a room at a very nice hotel in the center Disneyland. For an anniversary celebration, is that romantic, or would you rather be in a better location without the crowds but in a simpler, clean but basic hotel, for there is one and only one hotel on the shores of the Gosausee? There is no town or village or houses on the Gosausee, only one basic hotel with one of most awesome views in the world from its lakeside rooms. Having stayed overnight in both Hallstatt (once) and at the Gosausee (3 times) I don't even have to think about the choice.
.