What were the locations in this movie?

I don't know all the answers to your queationa but I'll do my best.

A far as the name of the palace, I'm not sure, but I'm fairly certain the one she breaks into is the same one in the intro when her grandma gave her the music box.

Yes, her grandmother really did live in France.

Sorry, That's about all I got. Hope that helps.

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I know this post is several months old, but figured I'd answer it (well partly, anyway). I believe the palace is St. Petersburg is the Winter Palace, where the Romanovs lived until 1917 (I think). It's still standing today. I can't help with the Paris one though, sorry :(

I know you asked this quite a while ago, so you may have already found some answers, but I'll post this just in case.

The palace in St. Petersburg (as an earlier poster said) is indeed the Catherine Palace, located 25km southeast of the city in a town called Tsarskoye Selo. And yes, it's the same one as in the first scenes with the music box :)

For the French part of the movie (and the real Marie did not actually live in France, but in Denmark, after the revolution), if you're referring to the palace where Marie tells Anastasia that Dimitri didn't take the money, it's not made clear whether this is even a real place. It could be the Grand Palais, the most famous Parisian palace (although it doesn't look much like it, admittedly. It cannot be Versailles since it seems to be located in the centre of town (Versailles is nearly an hour south of Paris).

As for the bridge, who knows! Movie logic ;) Judging from the horse statues, it seems to be the Pont Alexandre III, if you wanted to know which bridge it is. This means the palace could actually be the Grand Palais after all, as they're right next to each other, as shown in the movie.

Both palaces and the bridge do indeed still exist, too. Hope this helps!