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You do not 'go for a wander' in St P! You are only covered by the ships visa if you are on the ships tours, therefore you go where they want you to go. If you want more independence then book through a local registered guide like RedOctober, Alla, or DenRus. They may custom make a tour which includes shopping and your specific ballet.
No. A group visa means just that..you are covered by that visa as part of a group. If you want to wander off and do your own thing or go to the ballet on your own you will need to obtain your own individual visa. Personally, I would not go solo in St Petersburg, but your command of the Russian alphabet may exceed mine.
No, you can only go ashore independently if you have an individual visa. Immigration in St Petersburgh is extremely strict, you have to pass through this as soon as you disembark. We went ashore on several of the arranged excursions - Peterhof Palace is a must - and they always ended up in a very upmarket 'souvenir' shop that caters to visitors only (hence security guards on the door!) We didnt go to the Ballet but after talking to fellow passengers that had gone on the ship organized trip, they all said it was fantastic. If you do decide to get an independent visa, talk to the cruise line as they can take quite a while to organize (you often have to arrange them yourself). Enjoy.
If you really want to do this then I suggest you read an article in this Saturdays Daily Telegraph in which passengers on Aurora did their own thing. The link is http://www.telegraph.co.uk/travel/asktheexperts/1305446/Gill-Charlton-on-the-case.html otherwise go to www.telegraph.co.uk select travel and type Petersburg into the search box. List items in date order and select Gill Charlton - On the Case. Scroll down to the relevant article.