Horizons Unlimited - The HUBB - moscow, st-peterburg murmansk

I've never been on that exact route, but lived in Moscow for many years and have travelled a lot in Russia, including to Murmansk. You'd probably get more responses to this question in the part of the forum dealing with Russia, but I'll provide a few responses:
1) Moscow is an awesome city, but traffic volume and patterns can be horrible. I would strongly recommend getting a GPS map (fine OSM maps are fine) to guide you to your hotel, otherwise it might be a pain. I would recommend staying staying in the center; there is part of town called Kitai-Gorod which is old Moscow, where there are a lot of relatively inexpensive hotels, although you'd have to check about bike parking. Once you're there you can walk everywhere, and there are lots of bars and restaurants, etc. I would not stay outside the center, very drab and too difficult to get around. The center of Moscow in summer is absolutely glorious, with lots to do, so I highly recommend that you take advantage of it.

2) When travelling between major cities, if you're in a hurry you can take the major highway connecting the two, but it will suck. Lots of trucks and police, not pleasant at all. But if you have a couple of days, take the smaller roads through smaller towns for a much better experience.

3) There are places to stay all along the highways in Russia, everything from really grungy truck stops to fairly nice (by Russian standards) modern motels. I never planned ahead and was always able to find something, even in the most remote areas (including in the town of Vytegra on the road to Murmansk, where I found a wonderful little hotel on the banks of a small river with an outdoor restaurant, etc. But don't be too picky, because the number of such places is very limited. I tried to avoid the grungy trucks stops as much as possible, didn't get good vibes from most of them.

4) I would try to avoid interacting with drunk Russians, not much upside. Usually they'll try to get you to drink with them, but just excuse yourself politely, point to the bike, and hit the road. But at the same time, don't be paranoid...99.9% of Russians are extremely helpful and friendly, to the point that you suspect that they have some kind of angle...but usually they don't, they're just tickled to meet a foreigner in their town and would like to practice their English or invite you to dinner. Just use your situational awareness.

That's really about it, I would really just sort of go with the flow rather than having a super-regimented plan. Have fun!