Karlsplatz Square is one of the most famous in the city. It's practically right next to the Opera and the Exhibition Hall of Secession. We were standing before a very big square, with the occasional small stand in the middle. It's fountains and several attractions for children and older kids.
It's surrounded by the Secession building, for two other important constructions, the Technical University of Vienna and the Church of Saint Charles, the Karlskirche. This is the one of the most beautiful Baroque churches, with its impressive columns in the entrance and it's enormous green dome. Its dimensions trick you and it looks much bigger than it is.
Throughout the square (or park as some call it) there are all kinds of statues like a woman, child... that you can discover while walking through it.
The only problem you have is it's not one of the best places in Vienna to be at night or when it's dusk. It's not recommended that you're out late at night in this area, also because it gets pretty dark here.
It's better to go during the day when you can also appreciate everything much more. It has a metro stop right next to it.
As stated on the plaque in the square, "Mexico was the only country which officially protested before the League of Nations against the violent annexation of Austria by Nazi Germany." And it was for this reason that it was decided to erect the square under the name of Mexikoplatz. It is located on the banks of the Danube at the metro stop of Vorgaten Strase. It's right on the banks of the river, opposite the UN building in Vienna. The square, in itself, is not much to shout about, it´s only about 30 square meters, with its benches and other furnishings, but what is striking about it is the imposing cathedral, a peculiar style that is very reminiscent of those toy Playmobil castles, with rounded towers and almost perfect blocks. You can visit it almost every day, but the highlight is its exterior architecture, which has remained almost intact over time. It looks like it´s just been built. From the bridge which crosses the river, you can take beautiful pictures of the cathedral with the Danube river below. Far from being a tourist spot, it´s quite far from the center, but it´s not a bad idea to catch the subway and take a walk around. It is, at least, interesting and different from other monuments you will find in Vienna.
Schwarzenbergplatz may not be the most famous square in Vienna, but it's certainly one of the most beautiful. Located at the entrance of Karplatz, at the end of Renweg Street and near Belvedere Gardens, it's a spacious area with a large fountain in the middle that's sometimes illuminated in various colors. There's also a monument to those killed in the war where you can usually see flowers. The square is particularly interesting because of its location, in the middle of a street, among the cars, buses and trams. You won't often stop here on a typical sightseeing tour of Vienna, but it's still well worth a visit.