You can get to most sites in Munich on foot. They also have an easy to use U-bahn for farther distances.

There are many things to see depending on your interests -- palaces, churches, museums, markets, etc. If you mention what your interests are, you will get better responses.

I know that it is touristy and crowded, but I actually enjoyed having dinner (and beer) at the Hofbrau.

As for weather, you can check averages on a website like weather.com

As far as distance goes, you're about a 20-25 minute walk to the Marienplatz, where several of the beer houses are located.

The Hofbrau Haus is there, and, as mentioned above, not bad for a not so expensive meal. The restaurant is not on the ground floor.

On the ground floor is the main beer hall. Listen to the oompah band, which plays for 15-20 minutes and then takes a longer break. I know you're relatively young, but this is where Hitler got his start. Look up at the ceilings and see the ventilation system before electricity. Imagine Hitler jumping up on a table and firing up the half drunken crowd.

Don't miss the glockenspel in the Marienplatz.
http://en.wikipedia.org/wiki/Rathaus-Glockenspiel

Best bet to see it when it chimes is to find a good view from a cafe outdoors opposite the clock. Do this about 15-20 minutes before the scheuled chiming and order something. There will be a crowd that gathers when the clock does its thing. Just stand up and watch from your table.

There are buildings with views of the city from the Marienplatz. Check one or two out.

Stroll the Englischer Garten if the weather is nice. It's a very large park nearby. You'll see about everything from futbol matches to, possibly couples coupling.

Munich is a fun town with lots to do. I second (or third) the recommendation for the Hofbrau House. We have been to Munich several times and never miss it. The Viktualienmarkt is always fun too.
http://www.munichbeergardens.com/Viktualienmarkt

Be sure to visit the Asamkirche for truly over-the-top baroque (looks plain on the outside but don't be fooled -- we always call it the "awesome" kirche).
http://www.sacred-destinations.com/germany/munich-asamkirche

If you want to do a walking tour, Munich Walk Tour has lots of choices, and we have had good experiences with them.
www.munichwalktours.de

We have stayed at the Kings Hotel -- very nice! The room was a bit small (as most are in Europe), but I loved the beautiful canopy bed.

Since Munich is mainly flat, exploring the city on a bike is a good idea. There are guided bike tours (Mike's bike tours is one of the companies) but you could also just get a bike and explore the city on your own.

Check out thr river surfing on the Eisbach river in Munich.

http://yababoon.com/2012/10/17/river-surfing-in-munich-germany/

We were in Munich in mid June a few years ago and it was often overcast and a bit drizzly. Not super cold, but definitely want long pants and a light/rain jacket.

If you are interested in history, I would definitely consider visiting Dachau just outside of Munich. It is an easy bus ride to get there.

Here is a link to my blog with our trip report and pictures:
http://www.fromhometoroam.com/2012/06/munich/

Lots of great advice, marking for later

There are two King's Hotels, but as both are near the central station, you will be a central location anyway.
Catch the S-Bahn from central station for just two stops to Marienplatz. Or take tram 17 to Reichenbachplatz for easy access to Viktualienmarkt.

Hoping that you will have fine weather, and mid June can be anything from hot to barely warm, you will have the Augustinerkeller on Arnulfstr. in very close walking distance to either Kings Hotel. Your concierge will know that beergarden. Which is the only decently sized beergarden in central Munich and is a much nicer option on a warm June night than an indoor beerhall IMO.

Just a little beergarden etiquette:

Tablecloths signalize a seating area with service.
Without tablecloths you serve yourself at the outdoor booths for different types of food and beer (or softdrinks).
Most self-service sections feature long wooden benches and tables, so you do not "own" your table but should expect others to join. Or do so yourself on an "occupied" table if you can't find a totally free table.

In a real Munich beergarden, like Augustiner or Hirschgarten, you are allowed to bring your own food (but not drinks!) if you sit in the self-service section. Caveat: this BYO rule applies only in Munich beergardens, not everywhere in Germany or Bavaria, and not in outdoor seating areas of regular restaurants! When in doubt, just ask the people at the next tables.