The US has various forts and probably small towns as well, that are built (or restored) to give a sense of life in the 17th/18th/19th centuries. Fort Mackinac was my first thought, but I'm sure there are numerous others.
Have there been any attempts to do this with ancient historical sites? Some examples I was thinking of would be like a Roman border fort, or the Acropolis in Athens. Something where it's not just ruins or a current archaeological dig, but something that tries to recreate the architecture, colors, and overall atmosphere of an ancient site.
If there hasn't been much done like this, then follow-up question: what are the oldest full scale recreation/restoration projects? Oldest in terms of the time period. Renaissance? Early middle ages?
Full sites, not that I am aware of. There have been partial reconstructions, and the Nazareth Village tourist attraction is a reconstruction of a 1st century village complete with reenactors, though it is not a literal reconstruction (i.e. the foundations are not 2000 years old, it doesn't follow a site plan, etc, it just recreates the daily life of Nazareth in the 1st century).
Does the Nazareth Village thing fit what you're talking about? I'm not aware of any fully reconstructed ancient sites, but in terms of recreating daily life from an ancient time, the Nazareth Village thing is a good example.
There have been partial reconstructions at some sites in Israel, especially the national parks, such as the area A Late Bronze palace-temple complex at Hazor, or the high place at Tel Dan (which is one of the ugliest reconstructions ever).
I am not sure how to understand your reference to the Acropolis in Athens, but just in case: the Parthenon is actively being rebuilt. Also, in Nemea (mostly known for its lion), at least one temple is being (partially) rebuilt.