My friends and I stayed here as we were running the Riga Marathon. As a base for this it was excellent. The bag drop and the start line were 5-10 minutes walk away.
The accommodation is on edge of the old town which means so I can imagine is less noisy than if you were in the middle of the old town.
The flat is very secure. A passcode is required to enter the building and then there are two front doors and very sturdy.
Most of the tourist sites are within easy walking distance.
Plenty of places to eat and drink nearby but I suggest trying the Lido restaurants as they are very good value.
The tourist information office is very close and they are very helpful.
A real positive regarding the accommodation is that Number 22 bus from the airport stops less than 5 minutes walk from the flat. (1st stop after the river crossing)
I would recommend staying here.