One of the most beautiful public places in Europe, at least of those that I've seen, is Brussel's Grand-Place. The location was recognized by Professor Abe, GeorgeG, PortMoresby and GarryRF -- congratulations to all!
Grand-Place (Grote Markt in Dutch) is the central square of Brussels which is know of its beautiful and decorative architecture in a variety of styles (e.g. Baroque, Gothic). The square is lined by City Hall, Maison du Roi, and a number of guild houses. In 1998 it was placed on the UNESCO World Heritage list.
Many famous events in Brussels' history occurred in the Grand-Place, including the martyrdom of protestant leaders Hendrik Voes and Jan Van Essen, and a brutal attack by the French in 1695 targeting the façade and tower of City Hall, resulting in extensive damage to many buildings of the square. Obviously all has been repaired and today many of the buildings house museums and tourism-related shops.
Here are some of the famous sights of the square:
Brussel's Town Hall was built between 1401 and 1455, and is the only remaining medieval building in Grand-Place. Its tower is 96 m (315 ft) high, and is capped by a 4-metre (12 ft) statue of Saint Michael slaying a demon.
The tower is so tall that it's hard to compose a photo with the entire building in frame, even with a wide-angle lens.
There is a lot of elaborate carving on the façade of City Hall, including curious scenes of murder in some of the frames below.
King's House (Maison du Roi). Never home to a king, but it now houses the Museum of the City of Brussels.
House of the Dukes of Brabant
Assortment of Guild Houses. These represent various trade guilds, ranging from bakers to carpenters to archers to boatsmen. All of the buildings on the square have been beautifully restored.
Historically, dating to the 11th century, the square was a public market and to some degree that still occurs. Every day there is a flower market in the square, and a Christmas tree is placed annually. Concerts are held here and, most famously, every 2 years in Mid-August, the Flower carpet is exhibited in the square, being comprised of more than 500,000 begonia blooms. It is a sight to be hold as you can see in the following photo.