The "East Coast" is about 5,000 miles long Longshadow offered a sampling of possibilities, but maybe you want to narrow it down further to a region?

The historical significance of Boston and environs would certainly make Massachusetts a top contender - from the Pilgrims and the Mayflower through the Revolutionary War and commercial fishing.

For seafood, I'm partial to lobstah rolls; however, Maryland crab cakes are mighty fine also (Annapolis and Chesapeake Bay have history too).

Regarding your timing, anyplace in peak foliage may be difficult to find accommodations, though the season is nearing its final weeks in New England.

Savannah is very similar to Charleston in appearance and I usually refer to it as Charleston lite! It has good history and one thing Charleston doesn't have -- a really nice Train museum. They are close enough it would be easy enough to split time between them. They have Paula Dean's Restaurant and also the Little Bird Girl Statue that was made famous in the novel "Midnight in the Garden of Good and Evil". The Girl Scouts were originated in Savannah and you can see the home of the founder there.

As a visiting Englishman, I was blown away by Williamsburg. 1 day is to short, so get the 3 day pass (which we did). Don't bother with the 7 day pass, 2x 3 day with a decent pause in between much better in my opinion.

We have a lot of History here (so you tell us) but I have NEVER been to something similar done quite as well as this.
Lots of photo opportunity, but mainly architectural, if you ask the tradesmen many will let you take a snap - if you can understand 17c English. The attention to detail is astounding.

But don't think just of the photography. Get involved and move along as you (the audience) are unwittingly coerced into the story of your history by actors who don't so much guide but lead you into the next chapter.

In the unlikely event I make a return visit to the U.S., this place is high on my list of priorities - if not top.

Boston would have the advantage of packing a whole lot of history and beauty in to a small area, and one in which you do not need to bother with a car! You can get everywhere on the "T" and if not, the city is small enough that cab fare is not generally very much. The major attraction is the Freedom Trail, which takes you by old graveyards with many of our founding fathers, the Old North Church, the Paul Revere House, and takes you to the North End (Italian section - schedule lunch there!). The Freedom Trail starts by the State House, which is across the street from the Boston Commons and the Boston Public Garden. Well worth walking through.

Old Ironsides is an interesting visit. Walking along the Charles River on the Esplanade is great - they often have free concerts at the Hatch Shell, but it may be getting too late in the year for those. Wander around Harvard Square and the beautiful campus. The Harvard Coop for all your books, music and Harvard/MIT logo accessories!

MIT (on Mass Ave by the River - can catch a bus from Harvard Square) - is not a beautiful campus, but they probably still have a hallway dedicated to Doc Edgerton with large blow-ups of his most iconic high-speed photographs. It was upstairs in the main building where his lab was - you may have to ask for directions.

If you like baseball, there is Fenway Park. If you like garden spaces, there is the Arnold Arboretum designed by Edward Law Olmsted (think Central Park, Golden Gate Park, Biltmore Estate, and many others) - the Arboretum is the end of the "Emerald Necklace" he designed, which goes from the Esplanade, through the Fens (where Fenway Park and the Museum of Art is located) to the Arnold Arboretum.

Behind the State House is Beacon Hill - walk among the old homes and brick streets. Then head down Newbury Street for interesting shops and restaurants.

Have fun!

Since you'll have just four days, you'll have to limit yourself to one area. I would suggest New England. If you go after the peak of the leaf season, it will be less crowded and less expensive. Look at the links below and make a list of what you would like to see. Then check the distances between them and decide what you can do in a short time.

https://www.bing.com/search?q=what+to+see+in+new+england&cvid=67b1a8ec27f040a5be053d9eeacf2497&aqs=edge.0.0l3.5176j0j4&FORM=ANAB01&PC=DCTS