I have never been to St Petersburg but I would base your decisions on how likely you think it is that you will go back in the future. If you don't think you will be back, try to see all you can see realizing that you are skimming over the top of the iceberg.
If you think that you will be back, then I would cover a lot less but do it in depth. Seeing a palace or church in depth means that you wil not have to (unless you really want to) see it on your next visit. When we were in London the first time, we spent hours in Westminster Abbey. True, there were a lot of places we still haven't been to, but at least we know we have seen Westminster throroughly so will skip on later trips. Maybe you can skip the Hermitage if you know you will be back. Why see the hermitage if you spend less time there than they did on Amazing Race. I would love to take days.
We have a collection of top 10 books for many cities. Each book has dozens of lists in them. Although we try to prioritize and schedule our itinerary for efficiency, we realize that we are not going to see it all and don't try.