Vilnius is the capital of Lithuania.
When coming from Kaunas, still 10 kilometres or so away from Vilnius, there is a huge hypermarket, where you can catch a free bus to the centre. You can catch the same bus from the centre and start hitchhiking to Kaunas or Poland next to the market.
Trying to get to Riga you should take bus 5 (not really passing by centre but possible to find) to some of the last stops (there are a couple in the very beginning of the highway), alternatively to get onto the Via Baltica (E67) - the Tallinn, Riga, Kaunas road, get trolley bus 6 or 12 (and lots of other buses and trolleys, but I can only remember trolley 6 and 12 for definite) all the way to the end - about 100 yards from the end stop is the entrance to the main road that leads to Kaunas. Theres *always* other hitchers there, so its quite obvious the right spot.