Really interesting city - lots of things to see both in the city centre and some great palaces outside the city centre. Definitley take a canal cruise - the city is criss crossed with Canals and it's a great way to see it.
Of course you shouldn't miss the Hermitage / Winter Palace and the Peter and Paul Fortress in the city centre. On the outskirts the gardens and palace at the Peterhof are particularly fine ... Tsarkoye Selo is also very fine and there are plenty more palaces on the outskirts - bit akward to visit on your own but it's doable and there's plenty of tours as well.
Shopping wasn't up to much as I recall - eating out could be quite pricey too and not a whole lot of choice - Hotels are fairly steep as well.
Bring warm clothes as it's likely to be pretty cold (but probably no snow at that stage) - the wind there can be really icy and the days will be quite short by late october
Make sure you've got your Visa sorted out before you go - you still need to arrange a visa in advance for travel to Russia
A week is possibly a little long for just St. Petersburg