How flexible is your budget? I highly doubt you could find a Mykonos Town hotel with swimming pool for that price in August; if you could, it probably would require a 3 night minimum stay. Madalena Hotel has special rate availability for €112, but most decent hotels will cost you upwards of €150 per night (if you can find an Internet discount for direct booking on the hotel's own website) and many are well more than double and triple your budget. Kouros and Cavo Tagoo are well beyond your budget.
I suggest checking out Makis Place, which is situated near the new port at Tourlos. Their rates fall within your budget, and I have heard excellent feedback about the hotel from people who have stayed there multiple times. It's within reasonable walking distance of Mykonos Town, but there is a good taverna on site as well as excellent Mathew Taverna just a stone's throw away if you wanted to have dinner closer to your hotel and avoid walking the busy and narrow main road after dark. (A taxi ride either/both ways is always an option, though, and isn't expensive -- though taxis can be difficult to obtain during August.) Makis Place also is only a 15-minute walk from Agios Stefanos beach.
Edited: 7:19 pm, January 03, 2013