We go to Florida once or twice a year to visit my Father in law on the central East coast, but my wife grew up in Key West so we try and get down there every few years.

Diving for or bully netting lobster if you can get on a boat. I believe the season ends at the end of March, but there's a mini season in July before it reopens on August.

If you wanna try something different, go kill iguanas. They're super invasive, you see em everywhere.
https://www.iwannaiguanahunt.com/   

The key deer are pretty cool to see.
https://www.fws.gov/refuge/national-key-deer

Plus one for John PenneKamp snorkling.

If you're into birds at all, swing by the bird sanctuary
https://www.keepthemflying.org/

Touristy, but feeding the tarpon at Robbies is pretty fun.
https://www.robbies.com/

A little farther down from IM but not all the way to Key West cool local marina. Good food and drinks, and they rent kayaks. You can catch smaller mangrove snapper near the launch, especially around sunset. Might be some snook lurking around too, fun to catch pitching lures at the edge the mangroves.
https://geigerkeymarina.com/

If you get down to Key West but don't want to get jammed up in town doing touristy stuff, the Botanical garden is worth a visit.
https://www.keywest.garden/

And stop here for a Cuban mix, cafe con leche and croquetas on your way. Just order at the register with the rest of the locals and take em to go.
https://www.elmochokeywest.com/

If you're driving down from Miami, stop in here on the way. Great place to grab some Florida centric gifts, hot sauces, honey, jams and jellies and really unique fresh fruits. Don't forget to grab a fruit shake for the road.
https://www.robertishere.com/