We are back! Thank you for all the recommendations. Here is what we did in the end:
Vilnius (Thank you @wherecanifindteabags
Day 1
Arrived late evening. Bolt from the airport 12 Euros.
Day 2
AM Walked around the old town, climbed up to Gediminias castle, trekked through the woods up to the Three crosses (lovely views across the city from both places), walked to St John's church (amazing interior)
PM Free walking tour. Loved Uzupis and the university area. Had dinner at Gabi in the old town.
Day 3
Train to Trakai castle (4 euros return). Walked around the lakes to the castle, picnic lunch, tried kibinai pasties, tour of the castle. Lovely day out. Evening walk in the old town.
Riga (Thank you @Milkmani8)
Day 1
Arrived mid afternoon. Walk in the old town, stumbled into a free concert in St Peter's church, listened to an amazing cellist busker in the main square, traditional Latvian dinner (Province) in the old town. Evening walk along the river with a beautiful sunset.
Day 2
AM Free walking tour, late lunch at the central market.
PM Art Nouveau self-led tour in the early evening of all the beautiful buildings finishing with a walk along the river.
Day 3
AM Visit to the Russian Orthodox church (stunning), walked through Freedom Square then across the river to the National library. Visited the Agenskalns area and had lunch at the food market.
PM KGB corner house tour (15 euros). Excellent guide and tour, shocking place.
Tallinn (Thank you @Grumpyoldpersonwithcats, @pinkcrepuscule, @Fleecy, @ELS20 )
Day 1
Arrived mid afternoon. Walk in the old town up the Russian Orthodox church and up to the viewing points. Listened to the street musicians.
Day 2
AM Free walking tour
PM Walk to the food market in the Creative District, walk to the seafront to the seaplane harbour, people watching and ice cream!
Day 3
Bus 21b (2 euros) to the Estonian Open-Air Museum (18 Euros). Great day out, very interesting.
Helsinki (Thank you @ThisCatCanHop )
Day 1
Early morning ferry from Tallinn to Helsinki. Dropped luggage at the train station (8.90 euros for 12 hours)
AM Free walking tour, picnic lunch in the park
PM Ferry across to Suomenlinna island UNESCO heritage site (3.20 euros each way, island free to visit) coffee and cinnamon bun!, lovely walk around the island to the beach.
Evening: Visit to the Helsinki museum, dinner at Levant Boulevard (delicious Lebanese food), quick visit to Helsinki Cathedral (free after 6pm), train to the airport (4.40 euros) for 10pm flight.
Weather was 20-24 degrees most days, sunny and blue skies and perfect for exploring. Thank you for all the recommendations. Hopefully if anyone stumbles over this thread, it will help give some ideas too.