How high does an outside meter socket have to be?

Check with your electric utility company, as each utility sets the standards for there system. This is not a code issue. Most want the center of a meter 5 feet above grade, with a high limit of 5'6".

Down here they want center to be between 5' and 6'. I put at 5'6".
They also want a 4X4 or equivalent for ceiling fans. Many Electricians will use 2 2X4's and call it equivalent. I use Pressure treated 4X4, and there is no question.
I try to do things so no matter what Inspector it is, there is no question.
You can go higher with the Meter, so long as you have permanent steps.
Agree with above, Your local Electric Company should be able to hand you the requirements, and specs.