headed to CT coast from mystic and then headed west to DC. any suggestions on must eats on the way west ?

I've never heard Washington, DC referred to as west of Connecticut before. I have no suggestions for you.

DC is way south of CT - granted you have to go a little west to cross the Hudson - but it's definitely south.

For CT what is your budget and are you looking for lunch of dinner - and only near Mystic - or?

As the crow flies from Mystic CT to Washington DC.

approximate distance:
260miles west
165miles south

So the OP is correct, DC is farther west of Mystic than it is South.

About 40 minutes west of Mystic you will find, near exit 62 in Madison, Lenny and Joe's Fish tales, with very reliable lobster rolls. fish n chips, fried clams, etc. There is also a branch in New Haven, but I haven't tried it.

But also in New Haven, you might try their famous pizza at Frank Pepe's, Sally's etc.

Or, if you're brave, the Mexican food trucks lined up at the harbor. (I haven't stopped at them yet.)

Frank Pepe's also has a branch about twenty miles beyond New Haven in Fairfield.

Baltimore, Maryland - Ryleigh's Oyster in the Fed Hill Neighborhood is very good. Everything crabs, oysters and lobsters here is good.

An underrated move would be to go to New Brunswick, New Jersey and visit Rutgers University for one of their famous grease trucks. The most famous of them all is RU Hungry?, which is an experience for you if you wish to really pig out. Their fat sandwiches are inexpensive and are a Rutgers institution now. The Fat Darrell (Chicken Fingers, Mozzarella Sticks, French Fries and Marinara Sauce) and Fat Romano (Cheese steak, egg, Taylor Pork Roll, Fries, Lettuce, Tomato, Mayo and Ketchup) are the most popular sandwiches on the menu.

thanks to fra diavolo & itinerizer for answering my inquiry.
hope to try your suggestions