Great honeymoon choice if you're looking for fun but quiet. I don't remember Coconut Grove but Blue Wave is one that stood out in my mind for a place that was medium priced. We met people that had stayed there and were very pleased with the room at a decent price. Ask for the 2nd floor room right at the front so you can watch the sunrise from your balcony.
Blue Wave is closer to the North end of the village, so you'd be closer to the main swimming area at The Split. Caye Caulker isn't a big place, but this location would certainly make your walk to almost anywhere a minimal one.
We were there for 2 weeks in March and absolutely fell in love with CC. If you'd like more details, you can PM me as well.