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Peterhof is well worth a visit, but like everything else in Russia, expect to queue. We didn't go to the ballet, but people who did weren't very impressed.
Tallin is beautiful and easily explored by yourself, likewise Stockholm (Vasa Museum) and Helsinki (Stockmann's department store). We also visited Gdynia in Poland and took a taxi into town but got the courtesy bus back. Copenhagen is walkable from where the cruise ships berth, but only if you are reasonably fit.
Best buys - Crystal in Poland and amber everywhere.
Have a good time!
I booked with alla-tour.com and would happily recommend her and her tours to anyone.
Did a similar tour on the Braemar a couple of years ago, as my first cruise (but not my last!). The absolute highlight of the whole trip was the magical experience of the musical evening at the Hermitage. It isn't cheap, but was something very special. Beyond that, in Russia you're better off going with official tours, as then you're not worried about visas etc, but most of the rest is pretty explorable by yourself.
Peterhof is a definate must. The fountains in the park are wonderful. I was looking forward to the Hermitage but we were blessed with a very bossy guide who didn't allow you to linger. But the Hermitage is wonderful so is St Catherine's Palace. I did a full day tour of Palaces and Cathedrals in St Petersburg on the first day, an evening at the Hermitage. Then a morning at Peterhof and rounded off with an afternoon shopping at a flea market with the Cathedral of the Spilled Blood.
Helsinki is really nice and you can do the whole thing on your own. Fantastic architecture and all very walkable. The Finlandia concert hall is a real work of art.
Olso is brilliant but expensive. Buy a one day travel pass and you can get around easily.
Copenhagen is good and walkable. I spent a very nice morning in the museums - the museum of Denmark has some good Viking stuff in it.