Tver (Тверь) is a city in Russia, formerly known as Kalinin.
South/East towards Moscow
1) Take a bus number 10 and get off on the last stop. Walk 650 meters further to get to the nice spot. Half of the cars there go directly to Moscow.
2) Hitchhiking out of Tver in any major direction can be done at the same spot at a large roundabout on the Oktyabrskiy Prospekt street (Октябрьский проспект). This roundabout can be reached by all buses going into the direction of the South District (Южный микрорайон), I personally used the 223 from the city centre.
On this roundabout all cars drive moderately slow and they can easily pull over if you stand on the outer side a few meters before the road continues towards the south/west. Most cars drive to the shopping centre in the south/east of the city, but don't feel discouraged, all other cars are heading towards the highway to either Moscow (Москва) or Torzhok (Тoржок).
North/West towards Veliky Novgorod and Saint Petersburg
1) Hitchhiking out to the north is easier on the spot where road out of the city meets the ring road. You can get there on the bus 204. It's going from the train station, through the center, out of the city. Use Google maps or Yandex maps to find where to get it. Get off before the road merges with the ring road, you can hitchhike there. A lot of people go out of the city there, and I never waited for more than 20 minutes. There are plenty of space for any car to stop, including trucks.
If you are going to Saint Petersburg or further, get off where M10 road meets M11 highway. It's approximately 20 kilometers after the spot. M11 is a new toll road. If your driver doesn't go there, just get off and walk about 2 km to the toll gates and hitchhike from there. This highway is much faster than the regular road and you'll be in Saint Petersburg in 5 to 6 hours. In case your driver leaves the highway, I'd suggest to stay on it. This rarely happens as people usually go to long distances on this highway.
2) the same as second option in Moscow.
Other useful info
As always, write down the city names in Cyrillic! Russians can read the Latin script, but when they are driving fast (as they do) it might be too fast to read and understand your sign.
It's fairly easy find accommodation on Couchsurfing. Tver is quite a decent size city, but it's not touristic, therefore people will be happy to see other travellers, especially foreigners.