The DeutchesMuseum is excellent as well. Lots of stuff centered around the birth of "technology" and a huuuuge underground life size mining exhibit that spans multiple levels. Very cool if you're a geek like me.
MaximillianStrasse is their "Rodeo Drive" with a ton of high end shops. Lots of exotic cars usually parked right there too.
Regensberg is about 40min north, situated along the Danube river. The Altestadt (old city) in the center was not bombed during WWII, so it is entirely preserved with narrow cobblestone streets and a huuuuge gothic cathedral overlooking the stone bridge and river. Have dinner or a beer at AlteLinde Biergarten right on the Donau (Danube).
Generally, the smaller the restaurant the better. I love eating at the little mom and pop places that only have 5 things on the menu because it's usually "fantastiche!"