Another option would be to join a fancy-pants club in your own neck of the woods that has reciprocity with the NY Athletic Club ("NYAC").
Here in Portland, being a member of the Multnomah Athletic Club ("MAC") gets you reciprocity privileges with the NYAC.
I just checked, and MAC members also have reciprocity with the following clubs in Florida:
The Country Club of Coral Gables
997 N. Greenway Drive
Coral Gables, Florida 33134
(305) 448-7464
fax: (305) 448-0543
www.countryclubofcoralgables.com
The University Club of Orlando
150 East Central Blvd.
Orlando, FL 32801-2408
(407) 425-2514 fax: (407) 425-2517
www.ucluborlando.com
The Collier Athletic Club
710 Goodlette Road N.
Naples, Florida 34102
(239) 263-2566
fax: (239) 263-8725
www.collierathletic.org
I'm guessing that these Florida clubs also have reciprocity with the NYAC. If so, you may get more use out of joining one of them and using the NYAC reciprocity privileges when needed.
FWIW, MAC members also have reciprocity with the
"Penn Club" in NYC, which also offers nightly stays.
Just a thought.
-nodge