To hire a car (mini-bus) or to use a public one?
In general using public transport for tourist programs is neither comfortable nor efficient.
You will need to walk from the closest public transport stop while your private driver will bring you practically to the entrance door of the most
of the sites
Realistically speaking the metro is the only public transport which tourists can use. There are maps of it and navigation signs there and one can
work out which direction to take. But there are no metro stops next to Hermitage, Yusupoff or Catherine palaces.
So it is worth hiring private transport for the sake of comfort and efficiency.