Hi and welcome, Linamar. I am on the other side of Florida, but
@plantladylin might be the person who could direct you to a botanical garden in your area. But you still may have to travel a bit to find a large selection of different native orchids because some only grow inland, some grow further south only, and others need sun or shade or are high up in trees so can be hard to find. Hiking the nature preserves might possibly be more productive for you.
Another challenge you face in finding native orchids to paint is that most only bloom once a year, and for a fairly short season. Unlike cultivated orchids that bloom "on demand" you will only find for example the Encyclia tampensis blooming in the late spring, and the Epi. magnolia or "Green Fly orchid" blooms in the fall. They may be starting fairly soon but are extremely tiny and the blooms last for about a week.
So to help you search for orchids that will be in bloom, here's an excellent website:
http://flnativeorchids.com/nat... After you click on this link, then if you click each orchid name or picture the information page for that orchid will come up, telling you where to look for them, and what season they bloom as well.