You might do better using the bus for the trip - Valga isn't much of a tourist attraction, other than the fact that it is split by the boarder. I have family in the area, and can't think of any reason to go there other than curiosity, if the alternative is to spend longer in Riga.
If you were travelling by car then it could be a good place to stop for a coffee-break, but in your situation I would go for a direct connection if possible.
Hello! We're solving the same problem. There isn't any suitable direct connection from Tartu to Riga on Tuesdays, except for a bus very early in the morning, which is not an option. Does anyone know if there really is luggage storage at the Valga station?
Also, are the buses and trains in Estonia (between Tartu and Valga) usually on time? Thanks!
There is a luggage storage service available in the CargoBus shop, which is located in the bus/railway station in Valga. It's 1-3 euros per 24h to store luggage (price depends on weight). The service is open Monday-Friday 9am to 6pm, though they have a lunch break between 1 and 2pm.
Oh and about 99.5% of trains in Estonia are on time, and I've never been in a long-distance bus that has not been within 5 minutes of its schedule. Estonians are very punctual people, and of course it helps there is barely any traffic on the roads :).
Thank you very much Wout!