Unfortunately there aren't any really near Mayo itself. That said, the Flamingo Lake RV Park is a really nice site, about 25 minutes from Mayo mostly on the 9-A beltway. It is right off I-295 (3640 Newcomb Rd, Jacksonville, FL 32218-1510), 800.782.4323.
Since we live in Orange Park we've never stayed at Flamingo but many friends that have and all have enjoyed it.
Good luck with your treatments. We are both Mayo patients & love their care.
Mark & Sheila Heilman & The 3 Fur-Ball Princesses - Nikko, Mai-Thai & Andy
'07 MADP 4523, 2012 GMC Terrain SLT 2 wd
Blue Ox Alladin Tow Bar, M&G Engineering Dinghy Braking System