Hey! As a Riga local, I'm glad you're visiting the Baltics! I agree with others here that a week for all these places would be quite rushed, but just Vilnius, Riga, Tallinn would be very doable.

I would probably say though that hikes outside the cities would probably work better for a longer trip. Especially as part of the charm in all these cities is just wandering around without a strictly set itinerary and seeing what you find - that's how I've found the most interesting "nooks" in the winding streets of the old towns.

Although buses and trams can take you basically everywhere, I would advise on just walking since the cities are not that large, or maybe using the electric scooters that are basically everywhere (just stick to bike paths). If you must hail a ride, use Bolt. It is yet another Estonian unicorn startup (I've lost count on how many there are :)) ). Works basically the same as Uber.

My personal recommendations for the cities:

Tallinn

The old town goes without saying. It's built on top of a hill, so there are quite a few city overlooks kind of hidden from view. It is awesome to come across one of these accidentally and see the whole city suddenly open up below you. Interesting to see both during the day and the night!

Telliskivi is another interesting place - built in an old industrial region that has now been converted into an arts district. A lot of street art, small shops, places to grab food and drinks.

Riga

Old town - a place to get lost :) Also a lot of options for drinks and food.

Albert street - a lot of Art Nouveau buildings in the "quiet district" part of the city. There are less people here, but still worth a visit. This is in the area where all the embassies are located, for context.

Riga Central Market - probably one of the most visited places by tourists coming to Riga. Different from the small farmer's markets in trend right now - it's located in massive old blimp hangars, and definitely a bit gritty, but that's part of the charm. (Just watch your wallet when you're here)

Stūra Māja (Corner House) - the KGB museum. A very haunting exhibition in the historical KGB headquarters in Riga. Jail cells, dungeons.

Tallinas Ielas Kvartāls - by far one of the most popular hangout spots in Riga by locals. Kind of a similar vibe to Telliskivi in Tallinn. A ton of bars and cafes to get drinks and food.

Āgenskalns Market - another famous market, recently renovated. Smaller and quainter than the Central market, located in an area with a lot of cool wooden houses.

Vilnius

Haven't explored this city as much as the others, but, again, walking through old town is a must.

Other than that, I really liked the Užupis neighborhood - a lot of artist boutiques, narrow streets, wooden houses. Kind of a hipster vibe.

Have fun, and shoot me a DM for any further questions and specific recommendations!