If you are close to this city (if you are in Strasbourg, for example), or you are actually here in Nancy (the former capital of the Duchy of Lorraine), it's worth going to visit just so that you can see this square. A friend of mine told me that it was one of the most beautiful squares in the world, and although I had seen it in photos, it is even more spectacular in person.
This square was designated as a UNESCO World Heritage Site in 1983, which doesn't at all surprise me. Aside from how big it is, the most significant thing about the square are the golden doors that it has dotted around the entire area.
In total, there are four or five doors, but I cannot remember the exact figure. They give a "royal" air to the square, and I think that, if they weren't there, it wouldn't be as pretty.
Something else that I loved was eating breakfast in one of the restaurants situated in the square, whilst enjoying some delightful views. I tried the best French croissant ever there, which was freshly made, light and fluffy. That, along with my milky coffee, made for the best breakfast (typically French, of course) ever. I still remember it months later and I want to go back to Nancy just so that I can eat this breakfast in the beautiful square again. I don't remember exactly how much it cost me... I think it was somewhere in the region of 5€ or 6€, but honestly, we thought that it was going to be more expensive given how nice the area was.
Within the square, you will find restaurants, the town hall ("L'Hôtel de Ville'), the opera house and the Museum of Fine Arts. There is also a souvenir shop and a tourism office, where they gave us a free map of Nancy.
In the middle of the square, there is a statue of Stanislas pointing out the Arch de Triomphe that lies close by, which is also very pretty. However, in the past, where the statue of Stanislas now lies, there used to be one of Louis XV. At the base of the statue, there is an inscription that reads: "A Stanislas le bienfaisant La Lorraine reconnaissante".
The Arch de Triomphe is the most beautiful of all the ones that I have ever seen. It's by no means the biggest nor the most famous, but, for me, it is the most elegant and most beautiful. I think that's for the mix of the beige colour with the golden details for the statues that crown and surround it - the combination is stunning. This arch glorifies Louis XV and it has a golden medallion that is also dedicated to him. It was built in the middle of the walls that separated the old city from the new; the old city is the part found to the rear, and it's there where you can find the Porte de la Craffe and the Palais Ducal, amongst other places. The statues at the top represent peace and war and are related to the victory of Fontenoy and the Treaty of Aix-la-Chapelle. It consists of three arches: the central one is of an average size, whereas the ones on either side are identical in dimensions, just smaller. Besides, for the columns that it has and the distribution of the parts, it seems like it is actually divided on three vertical planes.
Don't forget to bring your camera! Without a shadow of a doubt, this square is the best thing that Nancy has to offer you as a tourist. And, if you can, try some Quiche Lorraine, which is typical of this region; I am sure that you've tried it before in other places, but I can assure you that it wasn't as good as it is here. There were also lots of bakeries that looked really good.
If you walk past the Arch de Triomphe, you will see a very pretty park to your right that is called Parc de la Pepinière.
I still really want to see the square by night, as it has to be lovely. From my experience of seeing places both during the day and after night has fallen, you see them differently: I guess that the lighting gives them another look. Also, I bought a postcard of the city at night with a cloudless sky and it is just breathtaking.
We travelled to Nancy by bus from Strasbourg with Eurolines, but, given that we were then going to Metz, the return transport to Strasbourg didn't work out as easily. In the end, we used the French version of BlaBlaCar (Covoiturage) to get back home. If you are going to Nancy, I recommend that you go to Metz on the same day because you will have more than enough time to visit the two cities and it ends up being cheaper too. Besides, it's only really worth visiting this square in Nancy and that's about it.