Most Belize banks will allow you to have your social security check deposited directly to your account with them.
But if you have a local bank account, that US dollar is going to get converted into the Belize dollar with a 2% conversion fee, and then that money will be sitting in your local Belize bank account, denominated in Belizean dollars. Instead of doing this, if you don’t need the money to pay for items in Belize dollars, you could just as easily have your social security check go into your foreign bank account, an offshore bank account in Belize, or international bank account in Belize. Those institutions will also accept those transfers or you can simply have your social security check deposited into your US bank account first, and then have it transferred.
One thing that you have to realize when you go offshore is that banking in Belize is different. Banks don’t have a ton of risk on your money, so they make money by charging fees. Fees tend to be a little bit higher when you get offshore. People in the US are used to having a free checking account or free savings account. When you go offshore, you are going to pay a monthly fee, typically somewhere around $12 to $15. Whether it is in Belize or somewhere in the Caribbean or out in the world somewhere else, you have a fee.
(For a discussion of what bank to use when you move to Belize, please see my answer under “When I move to Belize, should I open a bank account or should I open a bank account in Belize?”)