St Petersburg ... a few independent days

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Peterhof is a great idea and one to plan for a sunny day. You spend a fair amount of time going and coming in a boat (catch it at The Hermitage) and, of course, the gardens and fountains at Peterhof are best enjoyed in sunny weather. So watch the forecast before choosing the day for that one. St. Isaacs and Spilled Blood won't take long. The Russian Museum has wonderful works -- from icons through 20th century, if you have time. (It's very near Spilled Blood.) Another great thing to do is one of the walking tours. Go to the Peter's Walking Tours website. We found it was a great way to get an introduction and also to see some of the off-the-beaten track sites.

Second the nomination for the Russian Museum. I would actually prioritize this over the Hermitage.

One suggestion for navigating the rather extensive transit system- spend a few hours learning the Cyrillic alphabet. Your pronunciation doesn't have to be perfect, but it will help if you can read signs and roughly transliterate the names of stations and towns. The huge Stalinist gothic metro stations are almost an attraction in themselves, and the platforms use a unique loading system that I have never seen anywhere else in the world (you'll see what I mean when you get there). One word of advice when taking public transit in Russia- it is often packed, like nowhere else in Europe. Watch your valuables very closely.