Key West Lighthouse gives the best all-around view, across the street from Hemingway House.
If the weather is good, the ferry out to Fort Jefferson is a nice ride, visit the fort, snorkel if you want -- it is an all-day thing.
The Tropic Cinema is a neat art-deco movie theater [only one, Regal still closed from Hurricane Irma] that serves beer, wine, real butter, unique snacks.
A little "touristy", but if you have never been to KW, do one of the Conch Trains/Trolley. All the different companies are fine, pick any one.
Sunset drinks and/or tour at the USS Ingham [near Fort Zachary Taylor and Eco-Discovery Center].
Eco-Discovery Center is small, but free and free parking.
Fort Zachary Taylor requires admission, but nice beaches without being hassled.
Only one gun range in the Keys [not counting Key Largo], on Big Coppitt http://www.bigcoppittgunclub.com/ about 8 miles from KW proper.
Don