EZ Daze is a very nice park and I think it would be fine for an extended stay. Lots of facilities at the park (laundry, etc) and lots of shopping/dining in the local area. Google maps shows it is 18 miles and 25 minutes from St. Jude's. Not sure how long the pool stays open but you could call and ask them. Also might ask if they offer a special rate for people there for medical reasons....

It's a great RV park, open year round and they offer monthly rates. But be aware that in January you will experience very cold temperatures, it will often be below freezing (and even below zero) and there can be snow, so be prepared for the weather....