Hotel options are very limited in Mae Sai--especially if you don't have your own vehicle. (And if you don't speak Thai (or Shan or Burmese) your mobility is very limited in this town.) For foreign travelers without a car to spend a night in Mae Sai, Piyaporn Place Hotel is probably the best option. It is easy to locate; everyone knows where it is. And it is still within a walking distance from the border; you can walk around. I was pleasantly surprised by how nice and large the room was; I expected much less because of the price. And they have a decent international TV--again, not easy to find in Mae Sai.
This hotel is nothing special; it is not charming or friendly. But such extra qualities are so rare in Mae Sai; you would have to go to one of the "resort" places outside the town, for which you will need a car.