It's hard to think what 'exotic vegetables' are - it depends on where you live, I suppose. But to me, never having tried things like okra or jicama or kudzu or collards or salsify, these would have to qualify as exotic.
Your 'chayote' is our very common 'choko', either loved or despised! Many people grow their own vines here. I'm very fond of it, just boiled, then served with butter and pepper (I don't use salt). It's an excellent substitute for apples or pears in pies (or used to pad out a shortage of either), and it's very commonly used in pickles recipes in my part of the world. It's a fairly bland vegetable on its own, not unlike squash (not pumpkin) - so it readily takes on whatever flavours you add to it.
Here, we get a lot of Asian vegetables, now as common as the carrot or potato - bok choy, Chinese broccoli, kangkong (which I grow), choy sum, mizuna, daikon radish, tatsoi etc. I like them all. They are very, very easy to grow - and quick, too!
One vegetable you never hear about it the Manglewurzel. A variety of beetroot. I just love the name!
As long as it's not pumpkin or turnips, I'd probably like any vegetable, although slimy okra would have me a little nervous!
