Jack, I think you mean Neuschwanstein, not Hochschwanstein. It's in Hochschwangau or something like that.
But yes, it's horrendously full in summer. We found it well worth the visit though. It's the archetypal Central European castle, but full of Wagner motifs. Utterly bonkers! I'm assuming the OP will have rented a car, as it's tricky to get to by public transport otherwise.
There's another of Ludwig's castles nearby, which is much smaller and less impressive, but also less overrun by tourists. It's called Linderhof.
Most of the main attractions have already been mentioned: Viktualienmarkt, Englischer Garten in the early evening is best, my fave Biergarten is the one in the Garten at the Chinesischer Turm. Pop into the old Cuvilies Theater if you can - it was open and free of charge when I went, not sure if that's normal. The Alte and Neue Pinakotheken are fab, but teens might get a bit fed up if you stay overly long - mine would. If they're into cars the BMW Museum at the Olympic Stadium is meant to be a must. My fave district in Munich is Schwabing, which is To the left of the EG facing north - it's the 'university district' with lots of lovely cafes and small shops.
A day trip to Nymphenburg on the outskirts is definitely worthwhile.
Further out, day trips to Neuschwanstein and Lindenhof. The Zugspitze would be good fun for teens - take warm clothing for the summit. The three 'day trip' lakes fromMunich are Starnberger See, Anmersee, Chiemsee. If you all like a bit of a hike, I recall an amazing walk along the Bavarian/Austrian border, stopping off at a mountain hut for a pint of either milk or beer along the way. That was a day trip from Munich too. Have fun!