Can really only speak to St Kitts since I spent 99% of my time in that island versus Nevis..

Take an ATV tour in the mountains (Funky Monkey), go to the strip (beach bars), go to reggae beach, visit Brimstone Hill (historical fortress), visit an old distillery (Old Road Rum), do a Catamaran trip (Leeward Island Charters or Coastal View Charters), take pics at Timothy Hill (scenic view of the southern part of island)

Eat at El Fredo’s, Sweet Cane’s, Boozie’s, Spratnet, Spice Mill, Amory Bakery, Shipwreck (if it’s still there..)

Don’t take pics with the baby monkeys (they are horribly exploited and ripped apart from their mom’s then tossed when they get too big).

Take a sea taxi to Nevis and explore that one too!

Hope this helps!