The most popular sites are Booking and Airbnb. Personally, I prefer to book hotels/apartments via Booking. But also there are many good websites, you can check it out on your own. Here is the list of booking sites https://travelsites.com/booking-sites/
Was in St. Petersburg last autumn and it was an astonishing experience! I've too managed to visit the Hermitage, the architecture there is just fantastic. Booked a tour on https://petersburg.expert/tour/hermitage/, recommend it too if you're looking for any kind of tour.
Georgia is fantastic, agree, and Tbilisi is certainly worth visiting, I enjoyed it so much there. From the old churches to the local cafes in the town, the atmosphere is amazing, I didn't even know that it would be that good. You can see the photos of the tours for yourself here: https://onewaytour.ge/incoming-tours/tbilisi-city-tour/. We booked a tour through this site and very very pleased with the price and conditions. I'm still riddle why so few people know that this is a perfect tourirst location.