Fort Griffin
Historic site in Albany (vicinity), Shackelford County, Texas.
Each edition grades its towns against each other only.

Roughly 225K visitors a year make it to Abilene Zoological Gardens. Nothing on our list is inside Hawley; the 3 places to visit are within 40 miles. They include 2 museums and a zoo & aquarium. A longer outing takes you to Fort Griffin, 40 mi off.

Historic site in Albany (vicinity), Shackelford County, Texas.
The towns around it, and where to stay →
The map puts most of the 3 to the south.
Orange: Hawley. Numbers: the best-known places, matching the list below. © OpenStreetMap contributors
These 5 are within 60 miles, none in town.
Ranked by how many people look them up, so the famous places lead and the local favorites follow.
Fort Griffin: TxHC (talk), CC BY-SA 3.0 · Abilene Zoological Gardens: Keithimus (talk), CC BY-SA 3.0 · Robert E. Howard Museum: 0ccam, CC BY-SA 2.0 · The Grace Museum: Keithimus (talk), CC BY-SA 3.0 · Buffalo Gap Historic Village: Renelibrary, CC BY-SA 4.0