As Frank said, there is no ferry to Dangriga. There used to be one from Belize City to Placencia, but it no longer runs (don't think it did enough business, and the trip was long, wet and rough.)
I personally think you will benefit from renting a car. It's handy to have for exploring, the drive to Placencia down the Hummingbird is beautiful, most of the road is now paved and it's good to have a car on the Placencia peninsula since taxis are expensive and there is no regular bus service.
Besides Singing Sands (which is nice, should reopen soon with cabins better situated but without its pool) you might look at Green Parrot and Barnacle Bill's, both nice and moderately priced. I know Barnacle Bill's has reopened, not sure about Green Parrot. Closer to Placencia village, Kitty's is wonderful (it is open and the best beach on the peninsula). At the upscale end, Robert's Grove is fantastic.
You might also look at Hopkins, which had little storm damage. Hamanasi there is terrific. Nicest pool in southern Belize.
Dangriga offers little to the visitor, except as a jumping off point for the cayes. I wouldn't stay there.
Belize First www.belizefirst.com/