I liked Munich (see my Munich photos here) and feel it merits at least a couple of days, and you might even use it as base camp for a visit to the famous Neuschwanstein Castle. But if you are doing the run-go-see or are otherwise pressed for time, you can leave your bags at the Munich main train station, or Munich Hauptbahnhof right west of the city center where all the best attractions and popular beer gardens are.
Special Note: If you are worried the baggage storage might be full during peak season (Oktoberfest, for example) there is also a great luggage storage service similar to AirBNB that uses local businesses for your luggage. You can pre-pay and reserve storage before you even arrive. Check out Stasher to compare prices as well.
Storing luggage in Munich train station is a snap. There is an abundance of luggage lockers in the station easily found by looking for the luggage symbol on the signage above. I stored mine near the north exit right near the platforms.
The cost is 4 Euro per day for the standard locker, or 6 Euro per day for the rather large suitcase-sized lockers. There is a 72-hour limit. You pay for the first 24 hours to get the key to turn in the lock. If you return later than a day, you’ll have to insert money to unlock it. After 72 hours and the management may take your bags. The station is open 24 hours per day, and these coin lockers are accessible around the clock as well.
Tip: if all your luggage doesn’t quite fit in one of the 4-Euro luggage lockers, be sure to try the lockers in the bottom row, closest to the floor. These are just a wee bit bigger than the other 4-Euro lockers, but the same price. Otherwise, go around the corner to the 6-Euro lockers.
So, luggage lockers? Not a problem. Public restrooms? Good luck. Go before you get to the train station or get on your train and use that one.
Have a great day in Munich!