Moscow is far from being a pickpocketing capital like Barcelona or Naples and generally feels safer than many other major European cities. But there are several points to consider.
Good news first:
1. Walking in the streets late at night. “Late” time starts here later. 9, 10 or even 10.03 pm does not feel “late” - streets are still full with people going to/from a theatre or concert. There are plenty of people in the metro too. And even traffic cam be still heavy at 9.30 pm. Metro closes at 1 am – and then it feels late!
2. Wearing jewelry. Russians like to dress well and wear jewels where go to work or meeting friends. Wearing jewels in the center of Moscow is absolutely normal and should not be a concern.
However be aware of:
3. Places not to go. Outside its center, Moscow is pretty much the same in every part of it. There is no sharp social difference between its districts – it is socialistic times legacy. However the surroundings of some big clothes markets like Sadovod, Moskva shopping center, Dubrovka in the South-East feel less comfortable because of plethora of migrants and shadow economy. Another slightly unpleasant places are railways stations – homeless people, drinkers and gypsies are often attracted to here.
4. Pickpocketing. Moscow is very far from the pickpocketing capitals like Barcelona or Naples. In the streets or metro people feel relaxed about their belongings. However, touristic places always attract unwanted characters. Have your belongings in sight when you are in a queu to a museum or a theater, in a big group of tourists taking pictures and looking all in one direction (in a metro station for example or at the observation platform). Ask your guide about such places.
5. Look-alikes. People dressed like tzars, emperors, Lenin or Stalin offering taking pictures with them are those to avoid. They may look funny and offering a good price for a picture, but after the picture is taken they ask much more and can be quite pressing. Same can be said about people with doves, owels and so on.
6. Taxi. Use apps for ordering taxi. Uber, Yandex.Taxi or Gett will offer you much better rates, when just a taxi flagged down in a street. And by any means avoid taking taxi in the airport – high chances that you will end up being charged an enormous amount.
In any case it is always a good idea to have a private guide by your side.