Mesa Verde, in southwestern Colorado home of the ancient Anasazi people is pretty much the way that they left it in 1300.

http://www.nps.gov/meve/photosmultimedia/index.htm

Been there recently, Istanbul. Specifically the Golden Horn. Everywhere else was farm land hundreds of years ago and now there are some skyscrapers in Levent(a bit north west of the horn).

I'd say Venice as it has remained relatively unchanged since the 1400s.

This question is a poll or "throughout history" type question, which violates the subreddit rules. I have removed it. If you want to rephrase the question in a way that narrows the parameters you could repost it. I suggest something along the lines of "how much do cities in Europe resemble the way they looked in antiquity?" or "How different do the ruins of ancient cities in Mesopotamia look from the way they did when they were occupied?"

I like this question! Perhaps Udaipur? Founded 1553 as a new capital that would be safe from artillery, doesn't seem like much has changed. Definitely felt like a time warp when I was there. http://en.m.wikipedia.org/wiki/Udaipur

Pompeii.

Edit: Hasn't been inhabited since 79 A.D. but it hasn't changed a whole lot either. You could argue that it was "destroyed" by the eruption of Mt. Vesuvius but I think a lot of archeologists would disagree.