Easy, yes...if you just buy fruits, veggies, and fresh fish.....but its not cheap at all. Keep that in mind. My wife and I used to eat very healthy back in the U.S. and we spent about half as much as we do here. Greenhouse is great for a lot of things, but the prices are steep! Just want to make sure you are expecting that when you get here.
As for restaurants catering to it....there are very very few of the locally owned (and cost efficient) restaurants have no idea what healthy is and is not...I cant think of one that has been able to cook healthy when we've requested it actually. However, there are plenty of healthy choices here, but again, its usually the more expensive places. So, if you're trying to live on a Belizean paycheck or you are a budget minded retiree, then its usually not extremely affordable to do so.