Where can I play tennis in Moscow?

I recently had a good experience playing at CSKA up on Khondinskoye Polye. 

Luzhniki is the highest rated one among my tennis-playing friends, with American-style outdoor courts and even group lessons. Sometimes you will even see professionals on the courts. Here is a review of the court and the location. The site I just linked to also has reviews of other courts nearby.

Sokolniki is also recommended, with outdoor hard courts.

Expat.ru also has a list of courts in and around Moscow.