Thanks for the helpful info. Poorer neighborhoods are part of any big city, but am glad to hear it will be safe. I expect we will get laundry started and go get some food the night we arrive, so that the clothes have a couple days to dry. Looks like the next day is best for Schonbrunn. I am guess that will take most of the day? The Furniture Museum is between where we are staying and Schonbrunn, would that be worth a peek on the way back? Second day we will focus more on the center.
I understand the Hofburg is an entire complex and am not sure what to prioritize. We do like museums, history, architecture, food, coffee, etc. Probably won't be doing too much shopping as anything we buy adds to the things to be lugged around for the next four weeks or so. Wife and B-I-L are less into music concerts, so we probably won't be booking that. B-I-L was a city manager for years and is always interested in transit systems (we have traveled with him before), so he will be happy using transit. LOL An Argentinian friend that lives in Valencia, Spain loves Vienna and everything about it . . . maybe the pastries and public spaces most of all, so we are anticipating a nice few days.
For Schonbrunn, I think you can easily allocate most of a day if you plan to visit the interior and the gardens. I highly recommend visiting the carriage museum and I think the furniture museum is a nice pairing with everything. Nearby and also interesting is the Technical Museum. That said, I would definitely recommend after visiting Schonbrunn to take the U4 line to Karlsplatz for a visit to the Wien Museum (the best museum in the city, in my opinion). On the way you can pass through the Naschmarkt and look at the Majolikahaus and Secession Building.
Vienna isn't really known for pastries, but really for cake (and strudel). If you want good French pastries, however, there are some good spots. But for Viennese cakes/strudel, I recommend Gerstner (sour cherry or apricot strudel), Kaffee Alt Wien, Cafe Pruckel, Cafe Diglas on Wollzeile, Landtmann, Cafe Sperl and the takeaway window at Demel for Kaiserschmarrn. For public spaces, you want to walk around the Ring.
You might enjoy the food crawl I wrote up - https://community.ricksteves.com/travel-forum/austria/a-viennese-food-crawl