I wish I could remember where I'd read it, but recently I read that it takes about a hundred exposures to a food to become truly familiar with it. It seems like a lot, but I'm guessing that "exposure" means each bite or taste.
My husband's worked as a chef and has a much more adventurous palate than mine. My mouth is easily turned off by an unfamiliar texture or completely foreign taste, but I now eat almost all the things he does because he's found ways to acclimate my simpler palate to his.
For example, when he made soup, he'd add diced vegetables that were less familiar to me instead of the usual potatoes and carrots. Squash, turnips, and rutabegas made their way into the stew-pot, and because these unfamiliar foods were in a familiar context, I got used to and began to enjoy them quickly. If you already like a hamburger, try one with avocado, tomato, spinach leaves, or some other potentially burger-friendly food you'd like to appreciate more. You'll get acclimated and will eventually find your familiar food repertoire expanding.
You might also enjoy unfamiliar foods more if you pair them with something you like that's super-flavorful. Foods that I used to dislike got a liberal dose of cheese, garlic, and/or onions because those flavors overwhelmed the "oogy" stuff. Sometimes that kind of camouflage added to the calorie count, yes, but over time I could reduce the proportion of cheese or sauce to "oogy" food and it was no longer gross, but tasty.
Preparation may have a lot to do with how much you like a particular food. My taste buds are completely spoiled; I live in Food City, USA and I can't eat food that isn't prepared, cooked, and seasoned well. I cannot choke down a plain steamed vegetable to save my life; to me, they have the same taste and texture as the dirt they grew in. But oven-roast them, add them to stewed chicken and garlic, throw them into gumbo or curry, saute them with a dab of browned butter and finish cooking in a few tablespoons of chicken stock and they are
glorious.
Not all cooking techniques need to be time-consuming or sophisticated. Roasting does take some time, but it's as simple as tossing bite-sized pieces of vegetables with oil, salt, and pepper before scattering them on a baking sheet and putting them in the oven until cooked.
A lot of this is about vegetables, because so far I haven't found out how to like some of the other stuff I wish I could like (shrimp, venison, salmon). Maybe some foods we just can't cozy up to no matter how much we try; I will forever detest tuna even though I've tasted it more than enough to get "acclimated" to it. But I've found that even broadening my taste buds by a few foods hugely expands my dietary options and keeps me from getting bored or from missing out nutritionally.
Hope it helps, and if you'd like any specific recommendations, I'd be happy to get Mr. Nola to spill the (tasty) beans on some of his techniques.