We will be traveling to Munich at the end o f August for 3 nights prior to 2 weeks in Italy. We have 2 full days to see the sights, we are staying in the city center. With the limited time should we try to see The Residenz AND Nymphenburg Palace. Also since we will be seeing many art museums in Italy, is it better to just explore the city...take the RS walk, explore the English Garden, the market place etc?
Two full days is probably more than enough time to see both the Residenz and Schloss Nymphenburg. I haven't visited the latter, but the former took maybe an hour. It's a very large building, but many of the rooms are completely unadorned, so you move through rather quickly. And, Munich's center is relatively compact, so if your hotel is in the vicinity, it won't take long to get there.
I loved a 1 day itinerary I made up for my first visit to Munich. Although I'm a Rick Steves junkie, for Munich I used the Frommer's Walking tour (print for free on-line). The walking tour #1 takes you past all the main sights downtown and ends at the Königsplatz. From there you jump on the U and travel one (or two) stops south to the Hauptbahnhof. In front of the Hauptbahnhof you get on Tram #17, which will take you to the Nymphenburg Palace. Tour the palace then walk to the Hirschgarten, which is the largest beer garden in the world. They have an excellent food arcade and serve the delicious Augustinerbrau beer. If you have an interest in beer gardens, the return trip will take you right past the Augustiner Keller, another popular beer garden.
That would leave the second day for the English Garden, a second viewing of anything you liked the first day, etc. BTW, inside the English Garden is another popular beer garden called the Chinesischer Turm. Nice place to stop a rest a bit.
If you only have one day to explore the city, why not go on a real walking tour led by a guide who can tell you what you are looking at as well as answer all your questions. A lot easier than walking around with a book in your hand or listening to a recording. For 14€, you get a lot in those 4 hours. Alternative is a bike tour which will cover even more of the city.
You can easily visit Residenz museum and English garden (or at least part of it) in a couple of hours since they are very close to one another. Nymphenburg palace and parks are not in the center but you can get there by tram in 20 min. Botanical garden is next to the palace. Main Munich attractions are tightly packed in old town. In fact Marienplatz is just a few hundred meters from Residenz. You can just stroll along Sendlinger street and from Marienplatz to Karlsplatz and you will see most of them. Very near is Koenigsplatz and top classs museums Neue and Alte pinakothek. All of those and more in the film below so you can decide for yourself:
https://www.youtube.com/watch?v=_3ws7Axe6wQ
If you want a fun way to scratch a lot of the surface and sights of Munich then consider a Mike's Bike Tours:
If you want a good place for lunch with or without a beer (yes this has another beer garden) try the Viktualienmarkt. It is quite near the Marienplatz.