Hi Simon - I agree with RonS and his 3 recommendations, Roma, Discovery and Danae would all be fine. Roma is probably a bit out of the $50 price range and not worth the extra money IMO, the Discovery you can usually get a room for $45 a night or so (cheaper for the smaller single rooms on the interior). Its safe and has quite a nice roof deck, but is on a noisy corner. There's also the 'Ocean Breeze' a block south of the Discovery which is a small apartment type place, or a few blocks from there is Casa Pina casapina.net which is another small, safe little b&b type hotel (maybe 7 rooms or so). There's also Hotel Portes 9 which I stayed at a number of years ago when it was under a different name and ownership, so I can't speak to how the place is run these days but when I stayed there it was in nice condition, in a great location, and might be worth finding out more about how its being run these days (Hotels.com lists a $35 nightly room price which includes breakfast - I know because I'm considering it for my April trip). I think any of the above would meet your requirements.
I love going to the southwest part of the country, and if you make Barahona your jumping off point for that part of the country, I've stayed at the Hotel Caribe in Barahona on the Malecon, about $30 a night which includes both breakfast AND dinner (nothing fancy, basic Dominican dishes like Mofongo, fried salami, etc..). Barahona the town is nothing special, but San Rafael beach is about a half hour west of there, then past that Paraiso, on to the little town of Enriquillo - these all make for great places to walk, take pictures, meet locals, with few to no tourists. And Lake Enriquillo and Sierra de Baoruco National Park are inland from there, again with great wildlife viewing and photo opportunities.
