This has always been a good topic for discussion, so here's my two-cents.
When trying to determine the location of the City of Domes (the movie version, anyway), it's important to also know the timeline of the film's events.
At the beginning of the movie, the computer announces that Capricorn 15s are participating in that evening's Carrousel. The year of the city is 2274 (just for reference).
We can then assume that the film starts on a 15th 'Dome' day in the year 2274.
Later, when the film ends and Logan and Jessica go back to the Domes and try to get everyone's attention to escape the city, Computer announces that that evenings Carrousel participants are Capricorn 29s.
Hence, it can be assumed that a total of 14 days (2 weeks) have elapsed from the time Logan first meets Jessica until their return trip back to the Domes after visiting the ruins of DC. Logan and Jessica's only mode of traveling this distance would be walking.
The Chesapeake Bay is roughly about 30 miles from the center of DC. The Atlantic Ocean is around 90+ miles from DC's center. I always thought that the Domes were along the Delaware/Maryland coastline - probably near Rehoboth Beach, Delaware or Ocean City, Maryland.

However, Logan and Jessica must travel from the Domes to DC - AND THEN ALSO - from DC back to the Domes, all within 14 days - and still must meet this time requirement while traveling back to the Domes later with an Old Man who's carrying a walking stick!
Now, can Logan, Jessica and then later this Old Man all walk 90 miles to the Atlantic Ocean - and mostly barefoot - in less than 7 days (half the round trip)? Maybe....
But how about this scenerio (if we are trying to take the movie as being an accurate portrayal) - who's to say that the Eastern shore would be the same in 2274 as it is today. What if in the year 2274, thanks to the Global warming and the melting of the Polar Ice Caps, the Atlantic Ocean rose and the Eastern US shoreline we know today was altered due to the rising sea. Could it be that by the year 2274, the ocean moved inwards, towards DC - maybe even merging with the Bay - creating a new Eastern shoreline that's closer to DC? It's a possbililty and may help explain the time/walking distance issue a little more....
Thoughts?