Try the Five Points/Cookshop/Hundred Acres restaurants. They're all under the same owner and all pretty good. I wouldn't say that any one of them is better in terms of quality or focus than Zuni, though.
some time ago, i had just returned from SF and posted this:
156 10th Avenue, New York, NY 10011
31 Great Jones St, New York, NY 10012
38 MacDougal St., New York, NY 10012
That's an overly broad category. For example, Momofuku claims to serve "delicious American food", and I pretty much agree with the label—but that's another discussion. Joseph Leonard in the West Village is a place I've been to recently and was pleased by that could easily fit in your category.
170 Waverly Pl, New York, NY 10014
Can you describe a little bit more about what you're looking for, for people unfamiliar with Zuni in SF?
What do you mean by "sort of" like Zuni? What aspects do you seek, regarding service, atmosphere, price?
Are you looking for something like Mas or ABC Kitchen?
What's your budget for food only, and do you have a preferred neighborhood?