Moscow is one of the most expensive cities in the world, next to Tokio. However it is not the crew problem, because airline pays it. There are many very good (expensive, but good) hotels in the centre of Moscow. Security issue problem is a pure imagination. Once you have locked the aircraft there will be no suprising visitors. On that matter all Russian airports are quite strict.
There are some major airline crews doing a nightstop in Moscow, and none of them experienced any real problems. Yes most probably you would need a visa for a crew, but it is a very straight forward thing (1 year multi entry, you just need to apply). Or... let me tell you a secret: bizjet crews are receving visas upon arrival, you just need to pay some extra...