Travel
There are three airports within a few hours of Assateague Island National Seashore, so make sure you that view all three options when choosing a flight! Often, sites will allow you to search 'All Washington Airports' to look at pricing for all three.
The drive is not too bad either for those local! Check traffic before you go since there is really only one way to get to the Eastern Shore over the Bay Bridge, but as long as you are not leaving Friday after work gets out, you should be ok.
Flight
Baltimore (BWI) is the closest airport, but DCA and IAD are good options as well!
For all the days along the way