Speaking in general it’s nice place. Never met the problems neither with security nor locals during bird watching walks.
Last year atlas “Birds of Moscow City and the Moscow Region”
http://www.amazon.com/Atlas-Birds-Moscow-Region-Faunistica/dp/9546422622 counts for 273 species observed. At least one is missed (I met Arctic Redpoll, no in atlas, many times last winter). You will be at good season for bird watching. Pay special attention to large city parks. I prefer south-west part, e.g. Troparevo park. Surely you will meet here - Bluethroat, Robin, Nightingale, Redstart, Whinchat, three wagtails, some thrushes, Blackcap, many warblers, some flycatchers, some tits, Nuthatch (look for asiatica – often met during this year), Treecreeper, Red-backed Shrike, some woodpeckers, and many others. If lucky – Wryneck, Long-eared Owl, Corncrake (any case you will hear him). Btw, I’ve made cover photo of the referred atlas just in Troparevo.
You can subscribe for the forum
http://www.rbcu.ru/forum/ . Many of members are English speaking and we will provide you with more detailed directions.