Maui, Kona and Kauai all have extensive hiking as well as easy boat diving. Maui and Kona also have a lot of shore dive options. Cheap(er) local flights so you could do a week on 2 of them, each is different.
Chilly's suggestion of Belize also, do some dives off Anbergris then move to the mainland (puddle jumper or ferry) and hike in South Belize, there's the Mayan ruins, several nature preserves (jaguars, hiowler monkeys etc. Plus there's also some diving but the boat rides are an hour+ to the good stuff. Splash Dive ib Placencia can set it uo, pick you up at the airport and for diving and their sister company does the jungle toours.
For more money Hamanasi does both. Ajso Suthwest flies there direct from several US origins now,
Maybe the BVI;s also but not Cuan Law unless you wanted to mostly dive with a few hike options, some of the islands are pretty tiny.
It's actually not a bad land option, fly to St Thomas then Fast Ferry to the BV's. Lots of mountain hikes on Virgin Gorda and DiveBVI dives about 6-7 other islands. We went deep once all week but most dives were 40-80' Quie a few good wrecks also. Spend a 2nd week on Tortola - it's a long hillly island also. From either the fast ferries get you back to STT in time for a noonish flight - only about an hour ride/customs.
My nephew is an avid hiker/diver/biker. They did both in Costa Rica, even surfing. Somewhere near Guanacaste also.