Hmm - not sure how much any of these will push your envelope...
Yakko-San, a fantastic Japanese place in North Miami Beach, is a good place to start for:
Natto - a fermented soy bean product which has the texture of ... well, really sticky mucus if you ask me, served with tuna, squid, or stuffed in a tofu skin. More on natto here:
Grilled tongue (pretty tasty).
Chicken gizzards - sauteed or fried.
Uni - (sea urchin roe) often as sashimi, also in a pasta dish with ikura (salmon roe).
Mentaiko - cod fish roe, also in a pasta and possibly also in an onigiri (stuffed rice ball).
Also some of the fish they do are grilled whole with innards (there are a couple skinny silver-skinned fish they do this for, believe one is called sanma), gives a pungent bitter taste.
Lately they've had a special of glass-minnow nanbanzuke, which is a bowl of (whole) pickled minnows. Basically looks like a bait bucket.
Sometimes they have ankimo, which is monkfish liver (foie gras of the seas).
If you haven't tried it before, do a hamachi kama (yellowtail collarbone grilled); Yakko San will sometimes do other fish kama too, sometimes as a special they have a salmon kama and belly which is extraordinarily rich.
Grilled pork belly is now a regular on the menu there, though not particularly exotic anymore.
Another place where you stand a good chance of finding many similar items (and also some other good daily specials) is Su Shin Izakaya in Coral Gables.
Dim sum places are also good for finding some exotic parts. You should find chicken feet at most of them, and also have a good chance of finding tripe dishes. My local favorite for chicken feet is Mr. Chu's on South Beach. Also keep an eye out for shark's fin dumplings (minced and blended with pork). Other places to try include Tropical, South Garden, Kon Chau, all in South Miami.
Argentine Parilladas are another place to find some interesting parts. Almost any good parrillada plate will include mollejas (sweetbreads), morcillas (blood sausages), and chinchulines (pig intestines). For high end, the tops is probably Graziano's. For lower end, I like Las Vacas Gordas but mostly because it's a mile from my house.
At tapas places, keep an eye out for "callos" - a stew of morcilla, chorizo, tripe and garbanzo beans. One of my favorite places - El Carajo in the Citgo station at 17th St. and US1 - used to have this on the menu appetizingly translated as "Andalusian guts," not sure if they still have. Tapas y Copas in Coral Gables also has had on the menu before.
Hy Vong, a Vietnamese place, regularly has a tongue dish as an app and also often has a chicken liver and gizzards app too. There's another Vietnamese place off 163rd Street whose name escapes me, a somewhat dumpy place, that has a broad assortment of various parts (tripe, beef tendon, etc.) that you can get in your pho.
I believe Gourmet Diner on Biscayne Blvd. regularly has kidneys on the menu.
Ain't no bugs on any of these, but lots of good eats.
Mr Chu's Hong Kong Cuisine
890 Washington Ave, Miami Beach, FL 33139
13951 S Biscayne River Dr, Miami, FL 33161
Las Vacas Gordas
933 Normandy Dr, Miami Beach, FL 33141
El Carajo International Tapas & Wine
2465 SW 17th Ave, Miami, FL 33145
Izkaya Japanese Restaurant
159 Aragon Ave, Coral Gables, FL 33134
Graziano In the Gable
394 Giralda Avenue, Coral Gables, FL 33131
Tapas & Copas
98 Miracle Mile, Miami, FL 33134
Tropical Chinese Restaurant
7991 Bird Rd, Miami, FL 33155
South Garden Chinese Restaurant
10855 SW 72nd St Ste 10, Miami, FL 33173
Kon Chau Restaurant
8376 Bird Rd, Miami, FL 33155
Hy-Vong Vietnamese Cuisine
3458 SW 8th St, Miami, FL 33135
3881 NE 163rd Street, North Miami Beach, FL 33160
Following up on the subject of extreme cuisine -
An item I got to try recently at Yakko San would likely qualify - ika shiokara - also known as squid liver. This was on the specials board a few nights ago, and was only like $3.50, so ...
Well, unlike many other things I've had at Yakko San, I"m not sure this is one I'll be hankering for again. The presentation is basically a bowl of reddish-purplish-brownish viscera, with some thinly sliced cucumber for garnish. As you dip your chopsticks in, you discover strands of ... something ... later determined to julienned strips of squid meat. The flavor is ... quite funky ... it's goopy, it's salty, it's got something of a whang to it, it's got that sort of iron-y, liver-y type thing going on, together with a pungent seafood note. It's hard to decide whether the added texture from the squid strips is a positive contribution or not. I did indeed finish most of the bowl, mostly to try to discern what the appeal might be. It is quite a powerful flavor, something that would seem much more appropriate as a component of a sauce or the like rather than on its own. In any event, probably not something I'd volunteer for again, though it's always intereresting to try something new.
After the fact I learned a little bit more. Seems that it is indeed a fermented product which is heavily salted and then laid up for up to a month or possibly as much as a year:
If you follow these links, you will note that (1) both seem to emphasize the consumption of ika shiokara in conjunction with drinking (yes, a shot of whisky probably would have helped); and (2) it appears that opinion is decidedly mixed on the stuff, even among Japanese.
For some curious old ads for the stuff (which again, often have a drinking connection), see this link (need to scroll down a bit, then there are several) ->