Your trip looks like you have it quite filled up already with what's on your menu. That said, some random items mentioned above and a few not yet...
We did 18 days and nights, from Vilnius to Tallinn. So I'll leave out anything about Lithuania (you're not going) or Helsinki (we didn't go there). Of course, Tallinn is easy to love (love it soon, before the Russians go take it back). We also like Haapsalu a lot (don't miss the historic railway museum); we liked the nearby big islands of Saaremaa and Hiiumaa even more - though all those are off your planned route and you would need to trade something away to get there. We did not find Parnu particularly interesting.
In Latvia, we spent a couple days wandering Sigulda, Cesis, Turaida and enjoyed them all. Riga is the Big Kahuna, of course - or as called it "Prague without crowds." Be sure to spend some time in the big market (housed in and around WWI-era Zeppelin hangars!), and one could spend days wandering the old center gushing at the architecture. Everyojenswoons for Tallinn, and for good reason, but Riga is bigger and we felt had as many charms (which is saying a lot).
While in/around Riga, don't miss a side trip out to Rundale Palace, south of the city. It's an utterly spectacular baroque palace, in the same league as any other great palace in Europe (think Versailles, Schonbrunn, Nymphenburg, etc) - but without the crowds. There's a small, older castle (Bauska) in the same town which is worth a short stop but it pales in comparison to Rundale.
We drove all the way along the Baltic coast (along the Gulf of Riga, around Cape Kolka, and the open Baltic Sea) between Riga and Klaipeda in Lithuania. There is all sorts of weird abandoned Sovet Stuff around there, along with cute little towns, churches, and seaside relics. You probably don't have time but it was lovely and filled with all sorts of curiosities.
As for the car rental drop-off fee: Yes there will be one, but in our case it wasn't astronomical (IIRC I think about €100) which was acceptable to me as it allowed us the freedom to explore lesser-known corners even with a relatively short trip. YMMV. We found driving in the Baltics easy as pie (except of course parking in the old city centers, but that was only tricky in Riga and Tallinn, and in both cases we had modern hotels on the edge of the old center with parking included, so upon arrival we followed our GPS to the hotel, parked the car, and spent the rest of our time in the big cities on foot).
Even though you're going in summer, be prepared for some rain. We got several days (in July) that were pretty soggy and washed-out (and I live in Seattle so a little rain doesn't bother me).
It's a very cool, very under-appreciated corner of Europe. We loved the Baltics (and I seriously worry about their future).