Tropic and Maya will normally hold flights if an International carrier is late arriving, as a large percentage of arrivals at Goldson are in transit to San Pedro by some means or other, and a late arrival means the water taxi option is often not viable.
Which airline and where are you trying to get to?
How many in your party? Have you traveled in less developed counties before?
If you are alone and not familiar with Belize, a night in Belize City may not be the best start to a vacation, but for others, a $20 room at the Belcove with only a mattress, a fan and a few Belikins is a nice transition into another world.
Another alternative I've used a couple of times when there have been 4 of us was a night at Tonys in Corozal.
A nice hotel with a good restaurant at a price around half what the same style of accommodation in San Pedro would cost, but for transport up there you need around 4 to make it cost effective.
The Thunderbolt water taxi leaves Corozal at 7am and 3pm each day for San Pedro, and if you are going to be in a condo, try Kens Butchers in Corozal for supplies before hitting the island!
As I've mentioned before when questions such as yours have been posed, the more information given, the better the replies will be in addressing your concerns