I think the two places already mentioned, Manatee Inn and Tradewinds, are about the two best budget/low moderate spots in Placencia Village. Tradewinds would be my first choice, as it's on the water and this time of year shouldn't be more than US$35 or so double. Not large but pleasant (and cute) pastel cottages right on the beach.
Manatee Inn, about the same price, is new and clean, and it has a swimming pool ... but it's a "block" or so back from the water so it's a bit hotter, even with ceiling fans. The Czech couple who own it seem nice.
Other good choices in the village include Deb & Dave's (less expensive than either of the above), Harry's and Seaspray.
Belize First http://www.belizefirst.com/