I consider myself pretty lucky to have grown up in and visited some neat, historic towns on the coast. Here's some of the places I've visited (check out the hyperlinks for more photos):

North Carolina:
All of the NC Lighthouses


Wilmington - historic port city - former capital of NC:
USS North Carolina


Fort Fisher (1861-1865)

Moore's Creek Battlefield - Feb 22, 1776

Tryon Palace- Old NC Governor's house - New Bern - historic coastal city, former capital of NC


Biltmore estate - largest private estate in America - Ashville


Old Greenville tobacco market (largest in state-country?)

Wright Brothers First Flight Memorial- Kitty Hawk NC


Fort Macon - Built in 1826 - Morehead City, NC


South Carolina:
Charleston - historic port/coastal city - large historic district, old houses, roads, etc.:
Charleston City Market

Georgia:
Savannah (amazing pictures) - historic port/coastal city. Like Charleston, the city itself is a goldmine of history, but a lot of it isn't nationally known. It's like being back in the antebellum south:
Resting place of Nathanael Greene


WWII Memorial

Ft. Pulaski

Savannah's Famous Squares

Washington DC:
Pretty much everything that tourists do:
Washington monument
White House
Jefferson memorial
Lincoln memorial
WWII memorial
Holocaust museum
Vietnam memorial
The U.S. Mint (not that historic)
Arlington National cemetery - actually got to lay the wreath at the tomb of the unknown soldier with three other classmates.
the Capitol

Tennessee:
The Hermitage - resting place of Andrew Jackson


The Grand ole Opry house

Kentucky
Mammoth Cave- geologic history. Largest cave system in the world. Wikipedia says human interaction with the cave dates over six thousand years...I don't remember that from the tour and they didn't list the source, so who really knows.

I would like to visit Philadelphia and Boston some day to see some of the historic sites. Long-term I'd like to visit Ireland and Scotland to see some old castles and villages.