For truly tropical in February, might be tough to beat the Kona answer. Florida sucks for riding so that's out. I'd suggest Tucson or San Diego but in February they aren't exactly "tropical". But they'd be on the warm-ish side. The ONLY decent place to ride in Florida is in and around Claremont - to the north and west of Orlando. Weather in February is variable - can be awesome but you can also hit a cool to cold snap at that time of the year as well.
Tucson - has awesome riding options. Could go on and on about this. They just finished up a 130 mile bike path loop, that you don't have to cross any roads for I think on the whole of the loop!! Plus many great on-road riding options. Plus Mount Lemmon! Generally speaking at that time of the year, the mornings are cool to cold - can get down close to 0C at night, but will warm up rapidly into the high teens low 20'sC by mid-afternoon.
Kona - I was lucky enough to spend almost the whole month of February there this year. Awesome riding. Weather - amazing. It was my first time being there away from October, and I was really impressed. It's actually nicer in February! A little cooler, less humidity, less windy. Every day was almost a carbon copy of the previous day - Sunny, 30C and chance of an afternoon shower! However, this is mid-winter Prime-Time and accommodations are not surprisingly, tight.
Steve Fleck @stevefleck | Blog