First of all, Riga is a fantastic city, full of history and frankly worth a visit, especially in May when the terraces open and everybody drops their winther clothes.

As for the accomodation, I would not particularly recommend the Best Hostel Riga.

The entrance is located on A. Caka street, which is rather noisy. If you have a room looking towards the back it will be quiter, but you can leave the blinds closed as the only view is of cats fighting over the garbage bins.

Service is kept to a strict minimum, which means they barely say "Hello" but still say "Goodbye" when they sense you're leaving the country with your pockets full with unnecessary change. There is someone at the desk 24/7, so no need to stress about closing time.

Location is okay if you can be bothered walking 15 minutes to the old part of town or taking the bus.

Breakfast is not served. There is a vending machine in the lobby.

Bathroom is kept to strict minimum too, which is ok if you're staying for just 2 nights.
Overall cleanliness is good. Room was small and clean, bathroom too. Towels are provided and there is liquid soap in a dispenser in the shower.
The bed was clean and rather comfortbale if you prefer hard beds.

If you are on a low-budget trip through the baltic countries and don't mind the cheapest accomodation you can get (I mean "cheapest" in the postive AND the negative sense of the word), then you can consider staying there... but in Riga all accomodation are rather expensive, so I would look further first.
This is definetely not the place you come back to relax in the afternoon when you're on a day tour in the Old Town. You better find yourself a nice park bench to take a nap.