I was born in Russia and stayed in Leningrad for 3 weeks 15 years ago.. I'm sure that this place is much different today, but still some things will never change.

In addition to the tips of others, I recommend you:

visit of Petropavlovsky fortress - a few hours needed

Isaky monastery

Smolny monastery (City Hall and the staff of Lenin's revolution)

Letny Sad (Summer Garden)

some old passages

Alexandro-Nevski Lavra - the beautiful cemetery with some famous graves

a few boating trips on Neva and on canals

maybe you'll also be strong enough to see the open bridges at the night

Pushkin (the palace of Catherine the Great)

the palace of Peter the Great in Peterhof with beautiful fountaines(arrive there earlier, because at about 9 a.m. they open fountaines with music)

the wonderful! palace in Lomonosov

Pavlovsk - another great palace of Peter III

by train you can get to Petrozavodsk and from there on boat - to Kizy the island at the middle of the Onezsky Lake with striking wooden monastery built without using any single bolt. looks like made of gold

It's possible to walk in St Petersburg for weeks. I hope that you'll be able to make it justice during 8 days.

Have a nice trip.

Sincerely, Alex Elbert Jerusalem Israel