Miami, Florida, airport and FBO recommendations

I might have to attend a business meeting in June in Miami, Florida, and am
looking at flying my Bonanza from NY State to Miami.

Any recommendations for a preferred airport and FBO? Judging by the
comments on Airnav, it appears that Kendall-Tamiami (KTMB) seems to be the
most friendly to a single-engine GA pilot.

Also, what about weather in Florida during early June? I suspect that
t-storm avoidance will be the name of the game, but is there a better time
to fly (early AM or late PM) to have the best chance of getting into and
out of the Florida peninsula?

--
Peter