you should be able to rent something decent (with electricity and without insects) for 4,000 pesos/ month and more. for 2,000 pesos my guess is that won't be anything good...in good area...
on the other hand I heard that there are whole flats to rent in La Loteria for 7,000 pesos/ month....
so, like I said 4,000 pesos/ month is limit for something decent in my opinion.
in Las terrenas there are decent rooms to rent for 4,000 pesos, in other places in country, too... decent, but modest
Monte Cristi, Barahona, near the sea, whatever you want..... my guess is would be the same with Santiago. I paid 6,000 pesos/ month for room there but I overpaid that time ;-)
btw. Santiago is not place for walking, well at least it wasnt for me....