Usually Montezuma is pretty full at that time. At very least (as suggested above by Allylam), book a night or two. But honestly I would try to book your whole stay.
It saves you wasting a day of your holiday looking for accomodation. If you leave it to the last minute, you may get lucky or you may well end up paying a lot more or having a location either too far from town, too close to the late bar in town, or otherwise dodgy places.
I'm guessing you don't have a vehicle? Basically the further from town you can go, the more you get for your money, but then there is the inconvenience
I agree with the recommendation for Los Mangos or Amor de Mar, also Luna Llena. They are all kind of the perfect walking distance from town and within your price range. But I know Amor de Mar is already filling up.
1 thing for sure - book soon!