Hello there kkman and welcome to the forum. 3000 baht is cutting it close. The place across the street can get pricey depending on what "comforts" you desire.
There is a nice apartment right next to The Mall, with all the amenities, but again at a budget of 3,000 baht, it might be out of your price range. There are several apartment buildings all over the place, but I can't think of the name of them. There are some apartments just up the street from Assumption school on the street that the Pegasus Hotel is located. A lot of these places are on small sois though and not easy to find though. I'll ask the wife and post again here.