Babylon Villas #4 is a great place to stay in Ambergris. While the unit is somewhat spartan it's located perfectly, right next to downtown and on the beach.
Kitchen is very minimal, with very little in the way of food prep gear - but we ate out so we didn't care.
It's a little tricky to find from the street side, mainly due to the construction going on next door, but we just accessed everything from the beach side.
Chefy is a great host, meeting us at the unit and responding immensely to questions.