Thanks, Jeff. Having never been there, and only having minimal experience with Florida weather around Orlando, I'm kind of shooting in the dark for which months are the best ones to visit Key West. I appreciate the info.
When I think of Key West, (a rustic, island atmosphere, colorful cottages, and small-town ambience), I'm probably picturing what you're calling Old Town? And by the perimeter of the island, I assume you're talking about larger, chain type resorts? I haven't done a great amount of research about which places are where - for me, just coming up with a place to go to would be the first step.
I'm a Hyatt owner and turned my week into points. We exchanged into Hyatt Beach House in mid-January this year and purchased an extra day. It's correct that it is just at the entry to the island. However, it is a lovely spot with a small private beach and each unit has a view of the ocean and the pool, with lots of landscaping. We actually drove - six hours - from The Villages - an hour north of Orlando. But we were able to bring lots of food with us and basically ate all breakfasts and many lunches at the unit and most dinners out. There are buses that service the island but they have multiple stops and take over an hour to get downtown from the entry to Key West. However, we didn't have much trouble parking and occasionally we took Lyfts or Ubers. Among the things we did that haven't been mentioned here was a trip to Dry Tortugas National Park - an hour or two by boat. A wonderful place with superb guides who make the visit truly special. Another spot in walking distance from the Beach House was a wonderful botanical garden where we spent several hours across the bridge in Stock Island. Also, there is just across the street from that a great restaurant just on the ocean where fresh fish come in every day and the food is terrific (called Hurricane Hole). We went to the restaurant at Hyatt Sunset Harbor and it was awful and overpriced.
We also took ourselves on a home and garden tour, visited the Hemingway House, the Butterfly garden, the end of the US, checked into the Maritime Museum and several others and even found a play by the local theater group. Wish I'd seen these pages before as I didn't know about several of the opportunities you mentioned. It was super busy in January - sunbirds I assume - and hard to get the reservation into the Hyatt. I looked for exchanges but nothing came up and I was shocked by the prices of small hotels. We didn't much like Duval Street area at night. Way busy and crowded with cruisers and cheap stores. We were quite content to be at the Beach House. We had a last night celebration dinner at the Marriott (no restaurants at the Hyatt) that was expensive but phenomenal.