Not the person you're replying to, but I'm also a "try the local cuisine" person. A good percentage of the places I've visited have had some local thing that you'd have to really look for to find elsewhere. I don't end up liking all of them, but I like the experience of trying something new. Some specific examples:

• St. Louis, MO, USA: Gooey butter cake which is as gross and as delicious as it sounds.
• Changsha, Hunan, China: Stinky tofu. The local Changsha style of stinky tofu is completely unlike the more common style you'd find in night markets in Taiwan or elsewhere; it's only a little stinky but is dense, savory, and spicy.
• Singapore: Kaya toast. Kaya is a sweet coconut-based spread and they put it on buttery thick toast. I was addicted to this when I was in Singapore for work.
• Scotland: Haggis. It was... okay? Didn't love it, didn't hate it, don't see why it has the reputation it has.
• Jingdezhen, Jiangxi, China: Jiaoziba, which is a little local style of dumpling that's rich and quite spicy.
• Hiroshima, Japan: Okonomiyaki, a kind of savory pancake. Okonomiyaki is common in Japan but it's usually Osaka-style. The version they make in Hiroshima includes noodles in the dough.

In my experience, if you talk to a few locals, one of them will usually think of a local specialty and tell you where to try it.