The Airbnb experience I have had at Anna's was one of the best ever - the communication was smooth, I felt welcome, my room and the common area were clean, the kitchen was well-equipped and there were three toilets, two shower cubicles and two sinks for the guests to share. I highly recommend it and if I ever visit Riga again, I'd like to stay there.
There is a small supermarket downstairs and a bigger one a couple of hundred metres away. There is a cheap bistro too, at a stone's throw, open from 10am-9pm - in case you were peckish but didn't want to cook.
The Airbnb is situated 20 minutes (walk) away from the train/coach station. It takes a similar amount of time to get to town centre. It's on a busy street so it can be noisy if you leave your window (of room number 3) open.