The Opernhaus or Staatstheather (City Theatre) is a neoclassical building, an ancient royal court theatre, built in 1909-1912 by Max Littmann. It's made of sandstone and was restored in 1983-1984. It is currently the Headquarters of the Ballet and the Stuttgart Opera. It is just behind the New Palace, surrounded by gardens and a small lake. In the afternoon/evening they all look beautiful together. If you have time I'd recommend a visit to the opera. Especially for students. Every day, an hour before the opera starts, there's a queue of students waiting to buy tickets that haven't been sold. Only at the weekend might there be a problem getting a ticket. The tickets are reduced to $ 10 and if you arrive early they give out some of the best seats. The last time I went, there was 5 of us and we got an entire box to ourselves. On the way out of curiosity I looked at the price and my ticket was worth 110 Euros. Often you won't be that lucky and you may get seats all over the place. The only drawback is that the Stuttgart Opera is being renovated and it may be a bit modern for everyone's tastes. Otherwise it's 10/10.
This is where the cool kids hang out. The main square of the former gay/lesbian scene in Munich is nowadays the main spot of the trendiest part in town.
Things you can do: Meet your friends, have a picnic or just a beer, start your night out in one of dozens of bars around you or walk to the river and have a BBQ there. This square is not only nice to look at it is also the ideal starting point for exploring the trendy área of the "Glockenbachviertel"