There is a number of companies providing visa services, as Estonian citizen also require visa to visit Russia. One-time tourist visa costs ca 100 eur and will be ready in 4 days. You can stay up to 30 days. Different types of visas exists, also a multy-entry business visa.
There is very good connection with St. Petersburg, busses depart up to 8 times a day at reasonable price, typically 20-50€. Connection with Moscow is by plane, departs daily, priced 300€.