I have seen signs in some of the SVO lounges in Terminal F -- I can't speak to the new ones in Terminal D -- allowing purchased access for 1500 RUB (~$50), in case it's worth it to you. Totally not worth it for the Terminal F lounges; could be alright for the Terminal D lounges depending on your budget. They're much, much nicer than the old lounges, but I wouldn't call them world-class or anything. Also beware that Terminal D is still very much undergoing construction and thus opportunities for shopping etc. are quite limited.
In your shoes I personally would follow the signs to the AeroExpress (train to Moscow), which will lead you right to the Starbucks (near entrance to the AE train platforms). (Unfortunately you'll probably have to make this call before you decide to proceed to the Terminal D lounges, as I don't think you can easily pass back out security.) They have comfy seats though I'm not sure about wi-fi.
Whatever you do, do not eat at the Hippopotamus restaurant in Terminal D. It is execrable. There is a TGIF in Terminal D that's acceptable (it's standard TGIF fare, same the world over) and does, I believe, have free wi-fi.