Olga, isn't Hotel Tsaritsyno just one more metro stop south...very close? It may be a hotel-apartment meaning that you get some of the advantages of an apartment but not the price breaks. And I believe that Olga's suggestion of Hotel Orekhovo is also a hotel-apartment. Milan is likely to be very expensive.
Other nearby hotels: Eurociti and Eridan. Eurociti will also be very pricey.
Gator brings up a good point regarding apartments. Lots of advantages. However if this is your first trip to Russia and you don't speak Russian and you don't have one main lady, then maybe a hotel is best until you can learn to naviagate around safely. If you have a main lady however you might wish to enlist her help/suggestions regarding an apartment.
One caution: Some ladies could find the apartment idea offensive if you've never met and are asking her to help you arrange it. If she is modest, or if her family is cautious about your visit, then tread carefully on her assistance with an apartment. She may feel that you are expecting 'more' than simply help finding a place for you to sleep. Depends on the lady. It's a different culture...take nothing for granted.
As for taking a lady overnight in your hotel room, that has possible implications and you should find out whether the hotel allows it. Many do not, but others do. If in her neighborhood, she may not wish to be seen in your hotel. Usually the only girls who frequent Russian hotels are 'working girls' and we're not talking about the maid service. Finally, in a big city like Moscow the mafia likely has a franchise on the prostitution services offered via the front desk. Your lady strolling in/out and heading up/down the elevator to your room could be viewed as 'competition' for the working girls--a good way for your lady to have the crap beat out of her a few days after you've left town.
How you might proceed depends on a lot of finer details about your trip, who you will visit, etc.
Whatever you do, don't miss the newly re-opened Tsaritsyno Park and Estates!
Legend:
Kantemirovskaya (Кантемировская) is on the green Zamoskvoretskaya Line, south.
Here is a metro station map in English:
http://subway.umka.org/map-moscow/zamoskvoretskaya-line/kantemirovskaya.htmlMake copies for your trip. Maps in the metro will be in Russian but you can compare to get a feel of where you are.
Scroll down to the bottom, then come slowly from right to left. The third line is the dark green line. Move slowly upward (north) and you'll find your station.