Archaeology is actually everywhere you look, but it can be a bit difficult to find travel destinations related to archaeology. Here are some resources I’ve found. Some archaeological projects are what most people typically think about: studying ancient native American sites. But don’t forget that archaeologists also study more recent sites, such as presidential homes, historic towns (like Jamestowne and Williamsburg), battlefields, and more! Let me know if you know of other resources!
There are parks and museums all over the country you can visit to learn more about native peoples and historic sites.
Archaeological Parks in the US: Great resource by region and state of actual parks you can visit.
This page provides all sorts of great information about places you can visit related to archaeology.
You can actually participate in various archaeology digs all over the world. You can enroll as a student at some sites or volunteer at others.
National Park Service Volunteer Opportunities links
Archaeological volunteer opportunities for students and the curious