Jamestown Settlement, run by the Commonwealth of Virginia and a short distance from the original archaeological site, is the living-history museum: full-scale recreations of the three ships that brought the colonists in 1607 (Susan Constant, Godspeed, Discovery), a wooden fort with thatched buildings, and a recreated Powhatan village. Costumed interpreters demonstrate musket drills, blacksmithing, and Powhatan crafts.
It is unapologetically a museum for families and school groups, but the ships in particular — you can climb aboard the Susan Constant and stand on the tiny deck — give a visceral sense of the Atlantic crossing. The indoor galleries provide thorough historical context. Combine with Historic Jamestowne for a full day, taking the shuttle bus between them.