Not getting into a discussion of the realism of the whole thing. I'll just list what I know. What I'm discussing here is an unrealistically successful scenario for Russia.
The Russians would seek to either annex the Straits directly or turn them into a puppet state. They would be less than enthusiastic about letting the Greeks have them due to the presence of pro-English and pro-French parties in Athens and the implicit danger that they'd be inviting those powers into the Black Sea. They might change their opinion on this if
Nicholas of Leuchtenberg, a nephew of the tsar, is made king of Greece. They'd also want northeastern Anatolia (no state for the Armenians, don't wanna encourage irredentism in the other direction), southern Bessarabia (if this is after the Treaty of Paris), the mouth of the Danube, and maybe the Dobruja.
Concerning the Principalities, the feeling I got is that they renounced their expansionist aims there after the Crimean War - not counting the desire to regain southern Bessarabia, of course. But they'd want to keep them under their influence and as disunited as possible. A Russian prince (Leuchtenberg was discussed here too) or a native one with pro-Russian inclinations would be a bonus, either one for both or one in each.
I doubt they'd seek to annex Bulgaria, but it's the one place where they'd have the biggest interest and the best odds of placing a Russian on the throne, so they'd go for that. There was, around 1860, the prospect of Serbia coming under a Romanov, and that too would be preferred. The Montenegrins would get the Herzegovina and a southern extension into Albania. No idea on the likelyhood of a Serbo-Montenegrin union. I'm ignoring Austria here.
Concerning borders between Greece to the south and the South Slavs to the north, you'll have to wait until I get my notes on the line of division that Athens and Belgrade negotiated at around that time. It might take me a few days. The Russians wouldn't be too thrilled about it (the Greeks get quite a lot), but I think that they would acquiesce in something like it west of the Strymon.