What your neighbors would be like in Belize will all depend on where you live. For example, here in Placencia, people keep to themselves and do not really mess with their neighbors. They stay at home, not going out. However, once you go to Belize City or those places further up north on the peninsula of Placencia, the people there are sociable. They like going to their neighbor's house, having conversations, etc.
Well, here on the peninsula of Placencia, people are friendlier. Sometimes they are quiet, depending on the area, where you live, but most of the time they will be friendly, like people who do not seek trouble, not anything like that.
It is somewhat embarrassing to say this, but people who are not from Belize run 80% of Placencia. Many Belizeans live in Placencia, but most of the properties are run by people from other countries.
The majority of expats in Placencia are from Europe, America, and many other regions and countries. Expats and Belizeans live next to each other in one common neighborhood. People here in Belize are pretty much from all over the world. Most Belizeans speak English, so communication between English-speaking expats and locals is not difficult.