Of the "beaten path" sights, my favorite was the Church On The Spilt Blood. I also loved the Russia Museum - good choice! Don't miss The Wave by Aivosovsky, and be prepared to gasp. The Yusupov Palace is an intimate and liveable palace, if you can imagine such a thing, and the little theater is by itself worth the price of admission. I didn't have time to take the separate tour of the basement, where Rasputin was assassinated (or rather, where the job was started).
Of the less famous things, my favorite was the Sheremyetov Palace. It's another fancy villa turned into a museum of musical instruments, including some amazing tiny violins complete with videos of them being played. They also have an intact glass armonica (not a typo), which are rare because most of them have broken. The palace itself is great too; the highlight was the Etruscan Room. As a bonus, it doesn't get many visitors, so you can really enjoy it.
The Hermitage indeed has great art - by artists you can see in other museums. It also has crush load crowds. But the palace and the art is amazing. Your call.
Nevsky Prospect, despite its fame, to me was just a street (sort of like the Champs-Elysée). A canal or river cruise, on the other hand, is very nice, despite being a cliché.
The Metro is fascinating - unless you will go or have gone to Moscow, in which case it's distinctly in second place. Nothing can top the Moscow Metro. But if you're not going to Moscow, be sure to see St. Petersburg's Metro.
I haven't been to the suburban palaces myself, as they're not my interest either. So when I say I really liked the Yusupov and the Sheremyetov, know that this is coming from someone who isn't a "palace person."