You know, that thing/ingredient/specific dish on the menu you have to get. For me, there are several:
Howzabootchoo?
Too wide a question, as framed, for me. It’s the “must order”. So, looking at your list by way of example, I love sweetbreads but they are never going to be a “must order” just because they are on the menu. It needs to be a restaurant where I know the chef has the skill to not overcook them - which usually means somewhere upmarket.
Not dishes so much as ingredients, and of course it depends on the restaurant. But I am always drawn to: uni, crab, maitake mushrooms, monkfish liver, white asparagus, raviolo with an egg yolk inside.
Oh, maitake!! Yessss to all kinds of mushrooms, but def porcini, king oysters, and maitake.
That’s why I edited my list to be a lil more pacific 
Sweetbreads def only at ‘fancy’ places.
I used to always order tortilla soup at every new Mexican place to see their interpretation and how well they handled a basic staple.
Wide variance in execution.
I used to have similar policy with seekh kebabs in new South Asian places. One of those dishes where I’ve had good examples and bad ones - and know the difference.
Som tam and laab at Thai restaurants. Mapo tofu at Sichuan places. Carnitas tacos at, well, taco places 
Invariably tongue from a Mexican menu. Tongue sandwich at a proper deli if we’re not requesting two slices of rye containing chopped liver or whitefish salad, or a reuben. While hopefully checking the Bistro Jeanty (Yountville, CA) menu, we sadly noticed that a decades-long favorite of lamb tongue and potato salad vanished – what a difference a year makes.
Mostly seafood. Crab, clams, oysters, mussels, abalone, calamari steak, halibut, sole, even fish & chips. Swordfish is another story as I have yet to have it as good as I can grill it at home (provided I can get fresh swordfish).
In Thailand I ordered som tom thai with small salted/fermented crabs every time. Anywhere. Street stalls, restaurants, food courts, from a lady on a long slender boat at the floating market.
Thai restaurant (“Salathai”) in Vancouver, Canada only chicken basil cashew. Every time I tried something else I regretted it so the next time I ordered chicken basil dish again. Been there about several hundred times or more and never ate the rice but they still asked a couple of times if I wanted any. They never had anyone who didn’t eat rice with the dishes.
In Vietnam I asked scooter drivers where to eat Bun Rieu Cua (tomato soup with crab roe), and rice sheets filled with mince. They took me to their favourite spots. Pho is everywhere there. In Vancouver I ate pho in restaurants almost every single time. They were not competent at other soups. Had good rice sheet rolls in Vancouver. The shop manufactured the rice sheets for restaurants and they also served this dish in their shop.
In Sicily I must eat pickled aubergines and grilled aubergines kept submerged in olive oil.
In Austria it has to be Speck anything.
Regional foods when in Germany. In Mittelmosel at the moment it’s “Saumagen”/stuffed pig’s stomach, the “national” dish of Rheinland-Palatinate.
Squid
Chanterelles
Thick cut liver, cooked rare
Pasta with game ragu
Head cheese, or better still, simply head meat in vinaigrette
Andouillette
Fish and shellfish stews
Braised rabbit
There are a few ingredients that I love but rarely find. If I see them on a restaurant menu I order them. A probably incomplete list:
Bottarga
Fresh Sardines
Cardoons
Chestnut (Sweet or Savory)
Truffles (Budget Permitting)
Uni
Natto
Butter Melon
My list used to include shad roe and skate, but alas, they aren’t sustainable.
Anything with green chilis, especially Hatch.
Duck confit
Roasted duck
Own-fried dumplings /gyoza
Lobster rolls
Crab salad
Crabcakes
Palacsinta
Eggplant dip/melitzanasalata / babaganoush
Burek/ spanakopita/bourekas
Things made with artichokes.
Smoked salmon or spinach Benedict - I like comparing Hollandaise. I alternate Bennies with Huevos Rancheros as my typical brunch order.
My go-to Greasy Spoon order is a Greek omelette, typically with feta and tomato, sometimes onions, peppers or spinach are added.
I have been eating a lot of takeout breakfast sandwiches over the past 2 years.
I love artichoke dip and will order that instead of an entree if it’s on the menu… yes, I know, it’s out of date…
Broth-based soups, with lots of vegetables.
I tend to order seafood: shrimp, scallops, fish, mussels, oysters or any combination, broiled or baked instead of breaded and fried.
The only dessert I order is, in London, sticky toffee pudding. That limits me to my travels, once or twice a year.
Forgot about eggs benny. I can’t poach an egg to save my GD life, so that is an absolute must on the rare occasion I go out for brunch.
I’d have to go with eggs Benedict as well, uni, and seared foie gras with some fruit element.
Adding fresh sardines and natto to my own list. Have you ever cooked with the latter at home?
Depending on how they’re cooked (other ingredients with them) roast duck and lamb are my two gotta haves. But if the preparation/overall flavor isn’t to my liking after reading the menu, I’ll pass.
