The best budget option in the northeastern outskirts of town is this friendly three-room B&B, which offers basic private rooms and excellent Italian meals just for guests (think homemade ravioli and decadent tiramisu). Because it's so small, the whole place is often booked – be sure to reserve well in advance.
Rhina, the charming and thoughtful proprietress, speaks excellent English and is extremely helpful with organizing your stay in Santiago and onward transit. Naturalis Té is right across the street if you want a break from Italian (or Dominican, for that matter).