Starting with ones you can’t really find in the San Francisco Bay Area, but otherwise, in no particular order.
I haven’t been to Taiwan in a long time, so it’s surely changed some.

Raohe Street Night Market is where you get this.
On the topic of night markets, Raohe isn’t a priority. Shilin Night Market is the biggest and best, by far.
And Keelung Temple Night Market is also worth a visit, for the foodie.
牛舌餅 Cow’s Tongue Pastry

This used to be more common, decades ago. Now, the only place you can probably find it is the Shilin Night Market, if it’s still there. It’s a sweet, chewy pastry. The name refers to the shape.
Taiwan is heavily influenced by Japan. These “tire pastries” can be found in various spots, but the biggest selection of flavors used to be in XiMenDing.

奶油螃蟹 – Butter-steamed Crab
Now, they aren’t the Dungeness crabs we get on the west coast of North America, but it’s really good. Find this at the Keelung Temple Market.

鮮肉湯圓 – Savory TangYuan

The sweet TangYuan are ubiquitous, but savory ones can be found in Taiwan during the Winter.
藥燉排骨 – Medicine-braised short ribs

There are also lamb versions.
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By the way, Taiwanese vendors often overcharge tourists. I would exercise street smarts, or just happily let them fleece you a few extra bucks.
Haggling is expected at night markets for clothing. I often overpaid for things, only to find the same items on sale at Target, 2 years later, for less than I paid.
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Tshuah-ping – shaved ice
You can find this stateside, but it’s not as good, or as cheap.

This is really good, but it’s often served with intestine. Just eat the noodles and not the intestine.

米粉湯 – Rice vermicelli soup
Near Ximending, get this at 鴨肉扁 The Duck House (Goose) https://goo.gl/maps/STo8EUmALjmuhZg9A
Get a bowl of the rice vermicelli soup, and a plate of goose. The prices have gone up, but this restaurant has been around for at least half a century probably.

Fried rice noodles 炒米粉
The Hsinchu region of Taiwan is known for their super-thin rice noodles. You can find fried rice noodles everywhere. Taiwanese will top it with the same braised-minced pork that is served on top of rice.

Actually, the picture of the rice noodle soup above has noodles that are too thick. They should be the thin ones.
肉羹湯 – Rougengtang
“Geng1” is another word for soup, that typically denotes something thicker. Taiwanese like to adjust the taste by adding some black vinegar.

肉丸 – “Meatball”
This Taiwanese “meatball” is stuffed inside a chewy, starchy shell, served with a sweet sauce.

Might not be easy to find. But this thing is so good it’s started making its way to New York, etc. The best one used to be sold in front of a restaurant near National Taiwan University, on summer nights. But it wasn’t there last time I went.

Now, this isn’t my favorite. But it’s one of the most famous street foods. While you can get it in the US, it’s never the same.
You can find it everywhere.

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For an experience, I recommend taking the Gondola from near the Taipei Zoo, up to MaoKong. Enjoy the afternoon, have some tea and Mung Bean cookies (綠豆糕), and come back down at sunset.

Obviously, you need to eat this while you’re in Taiwan. I suggest eating wherever is popular with the locals.

臭豆腐 – Stinky Tofu
It’s an acquired taste for sure. The scent from the frying oil will linger on your clothes.

You can get this in the Bay Area now. But for a trip, go to JiuFen and eat them there.

By the way, JiuFen has a mask shop that I always regretted not going in to. You had to pay to go in, so I skipped it. But it was just like a mask shop from Ocarina of Time or Majora’s Mask or something. Blew my mind that it had a real life equivalent.
These will be good anywhere.

蛋餅 – Egg pancake
I’d get this from a street vendor in the morning, or a breakfast joint.

Get some soy milk too.
抓餅 – Zhuabing

Taiwanese bakeries are 10/10 awesome. My favorite, that you can’t find at home, is one filled with potato salad.

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OMG I could really keep going on and on. TL;DR: Halfcast, just eat the local cheap eats. Why are you going to Asia and eating in fancy restaurants :Joy: