We did Hawaii for a week after September 5th and it was *fabulous*! Granted, it was my honeymoon , but still-- the weather was balmly, there was only one light rain.... I would totally recommend it at that time of year.
We're doing a DW and HM in Mexico in September. We know it's hurricane season but are insuring our trip and wedding and hoping for the best. Just because a hurricane could happen doesn't mean it's going to. Lots of people go lots of places where crazy weather can occur but the odds are with them. Mexico is very inexpensive that time of year!
We went to Playa Del Carmen, Mexico in September and just got travel insurance in case it was going to be a wash out (cancel for any reason insurance). It rained hard a couple of times the first couple of days (not all day at all) and then it was sunny the rest of the week.