There definitely are some geocaches around Moscow that might be interesting to you. However you may luck the atmosphere of an abandoned object while visiting them just because it is weekend and the weather is good (well, more people then you expect, you know). The bunker mentioned by Filomena (the cache which I'm proud to maintain) is worth visiting but please mind what I just said. Due to specific limitations of the Russian variant of the game the have been no practice of placing geocaches within the bounds of the city until fall 2010; unlike their Western geocachers most of their Moscow colleagues lack experience of city caching. There are communities that focus on abandoned objects and I think you might look for a guide or at least an advice from these folks. If this doesn't fit your plans and you wish to go caching with some of guys from this community or by your own, I would recommend you contacting geocacher Dimkin on this website, he's one of those who (I believe) share your interests and is competent enough to give you a couple of places to visit. His profile is closed for all unregistered users so you have to register first to send him a message via this website. I sent him a message that you started this discussion - probably this would help (if he's not away for vacations).