I have never been to the one in Oviedo, although it's on my "to-do" list.
Right now I am trying to contact a person that I know that lives in Duverge and would know the Jimani market days. Also, I think you might be able to get out to Isla Cabritos in the middle of Lago Enriquillo from the town of Duverge, and there you could see big iguanas and possibly an american crocodile. I'll post what I find out about those things as soon as I get an answer, unless somebody already has one
If you are more of an adventure person, like hiking and want to see more of local life, I know people that could take you on a hike out to Laguna Cabral, to a small cave, out in a "yola" (boat carved from a tree trunk used for fishing in the lake), and you could eat lunch in a typical house. They have training on the local wildlife, but don't speak English. If I'm around that weekend I could go along to translate as I live nearby and wouldn't mind going out there again myself. Note: to go out on this lake, it would have to be earlier in the morning b/c later in the day the wind picks up more and the waves get too big for the boats to safely handle.
Here is some info about the Laguna Cabral:
Refugio de Vida Silvestre Laguna Cabral o Rinc?n
The person I know who can take you out there as a guide is Juan Alberto, a university student, and he is in a couple of the photos on that blog.