Novgorod Oblast is surprisingly sparsely populated for European Russia because World War II hit this region hard. Most of the former residents were either killed or forced to relocate permanently. But fear not, the cultural monuments of Novgorod were among the first of the Soviet's priorities for restoration after the war, underscoring their huge importance to Russia.
Novgorod's kremlin and churches are without question the highlight of any visit to the region, and probably the only destination on your itinerary for the region. That is, unless you love Dostoevsky as much as you should, in which case you should budget a full day to explore Staraya Russa.
Daily trains depart from Saint Petersburg to Novgorod in the afternoon and take 3 hours. The return trip leaves Novgorod in the morning around 07:00. A one way ticket costs only 300-350 RUR.
Daily overnight trains also depart from Moscow (around 22:00) for Novgorod (arriving around 06:00).
Novgorod is famous for its mead and rightly so—it's absolutely delicious.