linked below and should be helpful. The latter parts of October appear to be the best times. Toward the middle of the month crowds are heaviest - possibly due to Columbus Day Weekend and the food and wine festival being in full swing.
but be sure to get your ADRs done early. The last several years there has been "free dining" during this period. Crowds are low but ADRs are still pretty full.
Outside of that, the hurricane season is the only potential issue and I wouldn't have that change my plans.
I assume October is not a bad air rate time. I had to reserve a flight to Tampa St Pete less than two weeks from departure and the round trip cost was about $250 for a direct flight. I started looking a little earlier and had I been able to finalize my schedule the cost would have been $200.