Most of the larger car rental companies like Budget and Crystal have locations both at the international airport and in Belize City. Their prices are essentially the same, though a couple of places charge a nominal (seems like US$5) extra fee for airport pickup.
Some of the smaller companies such as Buy-Belize.com don't spring for an airport location and may have lower rates, though often you have to pay for a taxi to their location in the city. Keep in mind that local companies may not accept CDW waiver from your credit card company, adding US$10 to $15 a day for the rental.
You may want to get a quote from several places and see which one is lowest in total, taking into account daily or weekly rental, CDW and other fees, taxi, etc.