I had the same amount of time when I took delivery of my car and also visited Stuttgart. All of the museums especially the BMW one only need like 1.5hours to see the whole thing. Merc Museum took me a bit longer since it was absolutely massive. The Porsche museum is like an art modern art gallery and very nice. The public transportation in Munich is fast and easy to navigate.
Here's my list.
Munich:
1.BMW Museum
2.Olympia Park (I believe you get a free ticket to this via delivery services from the BMW museum)
3.Book the BMW factory tour
4.Explore the English Gardens and get some food at the Chinese Tower
5.Visit downtown Munich
6.Allianz Arena - I think is just a few stops from the Airport. You could hit that on the way to town. Tours are like 6 euro
7.Augustiner Keller was one of my fav beer gardens. Tons of people and friendly. Place gets busy during FC Bayern games
Outside Munich:
The Neuschwanstein Castle is another cool spot to visit outside the city. About under 2hrs away and I personally think is a must visit for a car pic and local eats. However, this is south of Munich and if you travel to Stuttgart from here it's another 4hrs. The Zugspitze is a big ass mountain thats south of Munich and Germany's highest peak. Pretty cool but a little pricey to go up. It's outside a cute little town called Garmisch-Partenkirchen. The back country roads there are absolutely beautiful. All of this can be reached by tour bus or rental car.
If you wanted to go this route it would be 1. Zugspitze 2. Neuschwanstein Castle 3. Stuttgart.
Stuttgart:
1. The Merc and Porsche museum can be hit in one trip/back to back.
2. Porsche drive. For like $300 euro they'll let you take out a 911 Carerra 4 GTS for 3hrs. I think they also do a driving tour of the city, which is more like a crazy drive out of cars and coffee. Pretty much everyone rents the 911s and line up outside. The sight and sound of like 15 of them tearing out of the museum is absolutely nuts. Staff is super friendly there and like to talk.
3. Explore Stuttgart at night. I found exploring downtown Stuttgart at night to be pretty awesome. The Schlossplatz is like the main square and the New Palace is lit up at night and stunning. During the day there's always something going on. I found a group of older guys (like 70+ years) playing bocce ball (or the German equivalent) that were heckling/hustling tourists. I spent like two hours with them drinking and playing despite the language barrier. lol
Drink the local beers and try and dine where the local go. I found buying food and drink at the grocery store to be way cheaper. I stayed near the central stations and would pop in there for a quick snack. The German's love their pork and chicken. The pork knuckle at the Chinese Turm was fucking awesome and the ribs at Augustiner Keller were great. I had to limit myself to drinking excessively which can easily be done since their beer goes down like water and you buy it by the liter. Dont be a pussy and order the half liter. :P
Enjoy your trip!!!
Anyways here's some pics I took from my trip of the places I mentioned above.
BMW Welt's delivery area and balcony overlook. That glass box to the right of the pictured car is the elevator where they bring your car up. Not sure if you're taking delivery but totally try and get a pic of your car coming up from the elevator if you are. It's like the factory is giving birth to it
lol
Allianz Arena
Zugspitze... on a clear day you can see the neighboring countries. Obviously I didnt have such luck.
Neuschwanstein Castle...take a tour bus here for a quick half day trip if you're not taking delivery.
The Schlossplatz in Stuttgart
