The greatest example of how modern arts in Moscow is evolving, what the modern lifestyle of young generation is and can give you many thoughts about Russia's development in general is Red October (a former factory, which now transformed to art-hipster-it district).
Red October is the district, which situated in the city center, on the island Balchug. Better search it according to the street Bersenevskaya embankment, metro Kropotkinskaya.
The Lambada market on Red October attracts lots of young creative muscovite. It is the market of local Russian designers, who sell clothes made on their own, some vintage things and of course many accessories. What is more such events attract so many beautiful people plus music, nice atmosphere and fun - a great mix for a best weekend in Moscow!
Almost every weekend there is a food market on Red October. Many local chefs, small cafes and catering businesses had an opportunity to sell their food! Making burgers right on the open fire. Various pies, curry, fruit from farms and hundred types of lemonades in giant jars.
This format of events is very new to Moscow and to Russia in the whole. So you have to be here to feel this freshness, joy and liberty!
What else you can do on Red October?
Strelka Summer School - it is a range of lectures and master-classes, which are opened to the public and are free. Most of them have thrilling topics to discuss and are around urbanism, architecture, media and design.
Also Digital October ("place of globally-minded technology entrepreneurship community") organizes many events around technical startups, new media and tech-entrepreneurship topics. Some of them are free. Otherwise just check the corridor which leads to their office space - it is the small museum the list of milestones in tech-sphere (when did the first computer virus appeared? who was the first person in USSR to use the internet on a regular basis? etc.)