We did a trip through the Baltics in July a few years ago, just under three weeks (Latvia, Lithuania, Estonia, with a few days in Krakow and Warsaw on our way home).
We rented a car (picked it up in Vilnius, dropped it off in Tallinn), and were glad we did - it gave us a chance to break out of the just-the-three-capitals route that many visitors limit themselves to. Driving in the Baltics was easy, delightful and rewarding, and allowed us to explore out-of-the-way places. If you are limited to public transportation, you can still reach many places, it just might take more time.
In Vilnius, look for the "old" neighborhoods; we found one that seemed to be the old diplomatic quarter (embassies and consulates from the Soviet era), with a beautiful orthodox church, and old housing stock in every state and condition you could imagine. We wandered through rows of old "collective" housing units that were fascinating (some dilapidated, some with lots of character). Don't miss Trakai, less than an hour by car outside the city (an impressive castle/fortress on an island in a picture-perfect setting).
We didn't spend a lot of time exploring Klaipeda, since when we were there it rained heavily and steadily for 24 hours (worth noting - this was in July - be ready for some rain). The Curonian Spit was tempting but the atmospheric spit gave us reason to move along to the north along the coast - an area which was lovely (tho probably not easily accessible without your own car).
Riga is a great city - if you love architecture, you would be hard-pressed to find a more interesting mix, everything from medieval to Soviet. It's easy to spend days wandering the streets of the old city. Check out the sprawling and lively city market housed in old WWI-era Zeppelin hangars. For day-trips, don't miss Rundale Palace, it reminded me of other grand European royal palaces of the time - Versailles, Schönbrunn, and Nymphenburg - except without the crowds. We also enjoyed Sigulda, Turaida and Cesis. Not sure how easy it would be to do without your own car. The coast along the Baltic and Gulf of Riga are quite pretty if you can get to them.
Hope you get nice sunny weather but be prepared for driving rain, just in case.