I don't know how many times I've plopped some part of an animal into a pot with no specific intent in mind. I just know that if I tenderize the piece of offal or meat, I will figure out the rest later. Trippa alla Romana requires long-simmered tripe. Pig's ears salad (see versions here and here), or pig's ears seared in a cast iron, both require the ears to be simmered beforehand.
Once the parts are tender, you can do anything you want to finish the dish and give it character—by deep-frying or pan-frying to crisp up skin and flesh, by roasting or broiling, and so forth. When cooking the cheaper cuts of the animal: necks and feet, stomachs, tails and tongues, the game plan is always: a) Make it tender b) Add flavor and texture.
Now that the weather is getting so nice, you may not want to spend too much time in the kitchen at all. You may simply want to take your well-simmered animal parts and move them to the grill. Here are just a few options.
Tongue is a stress-free option for the grill. You simmer the tongue in water or stock, adding aromatics and spices. If I'm really pressed for time and mental reserves, I may do nothing more than plop a tongue into a pot with water and keep the heat on low. A few hours of simmering does the bulk of the work. Then you peel the tongue and cut it into thickish slabs, perfect for tossing on the grill. Because tongue is so fatty, you don't have to worry about it getting tough or dry.
After grilling, serve the tongue in taco form, or drizzle on some kind of sauce or garnish, which could be no more than a mixture of olive oil, salt, and scallions. (Or, make chimichurri sauce or salsa verde, if you are so inclined to whip up a batch.)
Option two: Grilled Pig's Tails. Same principle here. Simmer, then toss it on the grill. The only difference here is that you want to use a more indirect flame so you don't get too many flare-ups when the pork fat drips down into the grill. Serve with a sauce of some kind, or just freshly ground black pepper and salt.
Other suggestions: Grilled trotters, grilled ears, grilled snouts, grilled hocks.