We’ve been to Tallinn once and to Lithuania three times. Unfortunately, we’ve not been to Riga other than the bus station and the airport. In Tallinn we pretty much followed the RS guidebook. He has, or at least did a few years ago, a section on Tallinn in the Scandinavia book. We did the “self-guided walk” and because of time stuck to downtown Tallinn.
You’ve probably discovered that there aren’t many guidebooks for Lithuania. One source of information is the In Your Pocket guides-Reader’s Digest sized booklets covering many European cities. Most of the info is free online at inyourpocket.com . Vilnius has many churches that had been anything from gyms to auto shops during the Soviet era. So learn their history. There’s a marker for the Baltic Chain (human chain connecting the 3 capitals) in front of the main cathedral. The infamous TV station the Soviets attacked in 1991 is worth a short visit. There are many museums, including ones unique to Jews in Lithuania and another to the KGB.
Just outside of Vilnius is Trakai, a castle built beginning in the late 14th century. Between Vilnius and Kaunas is Rumsiskes, a Lithuanian open-air ethnographic museum. On the outskirts of Kaunas is the Ninth Fort and a giant memorial to Jews that were massacred nearby. Just north of Šiauliai is the Hill of Crosses. This would be easiest to visit as a stop between Riga and Vilnius.
The food is good. Not much beef. Try ‘cepelinai’ a national dish.
If choosing between bus and train I’d probably go with the bus—nicer, faster.
Have a great trip.