Plaza de la Puerta del Sol

The Plaza de la Puerta del Sol is Madrid's most central point, in fact, there is a marker that indicates the point "0 km". The distances along the highways all across Spain are all measured from that particular point.
There is also an interesting statue of a bronze bear nuzzling a madrono tree. It's the symbol of the city and one of those "must see" landmarks. At night they have various bands playing in the plaza – one was a group playing music very similar to the Andes music from Ecuador. Everyone stood around listening to them for a good hour at least. This little bear is so well known it's used as a meeting place for people...course then you can't find your friends because EVERYONE is waiting there.

There's no such thing as an early dinner in Madrid. In fact, most restaurants don't even open until 8:30 and 9:00 is far more common.
My most interesting meal was in an Argentinian restaurant where I ate Italian pasta while listening to Chinese music. Quite an international experience. They also had a very nice vegetarian restaurant with natural foods native to Spain.