This is right up my street and if I had any leave left I'd be booking it.
A lovely break to Riga and Tallinn. Arriving into Riga early morning on 9th February you will stay at the 4* Rockwell Gertrude Hotel for just 1 night. This hotel is centrally located and near the old town and attractions. It also has great reviews and breakfast is included.
On 10th February you have another full day in Riga, so although you are there for 1 night you can have 2 full days, and then later on you will catch the amazing value Lux bus to Tallinn. These are really nice buses and look comfortable and great value for €3pp. There are various departures thoughout the day some €5 so you can see which departure suits you best if the one in this deal doesnt.
In Tallinn you will spend 2 nights (or you could adjust this deal and spend 2 nights in Latvia and 1 in Tallinn but I've read Tallinn is much nicer). In Tallinn another good value hotel, the Economy hotel right near the old town and public transport. Again, this has good reviews and breakfast is included.
2 one way flights London to Riga £33.98 book at Ryanair
1 night in Riga £33.26 book at Expedia.
Bus from Riga to Tallinn for 2 €6/£5.15 book at luxexpress.en
2 nights in Tallinn £46 book at booking.com
2 one way flights Tallinn to London £38.05 book at Ryanair