There are actually two B2 hotels in Chiang Rai town. The first one is located at the night market area while the second one, where I stayed, is located not too far away from the first one. There was a blessing though for (mistakenly) choosing this one as I managed to find a mosque and a market during my exploration of the town.
I must say the rate is very reasonable, especially when the room is very spacious. What more, the town is just within a walking distance. However, if you ask the counter staff, they would suggest you to take a taxi.
There is nothing to complain and I would recommend this place to people who are visiting Chiang Rai in the future.