Re: "modern Godzilla" - You're thinking of the 1998 movie, no doubt. Almost everybody agrees that the monster from that movie is an entirely separate character from the Big G himself. The 2014 version, which was a lot more faithful to the spirit of the original, turns up in San Fransisco, though it's to fight a different monster rather than to destroy the city itself.

So yeah, visiting Maryland would make no sense unless he either: a) swam all the way around South America, which would've taken a few weeks at least, or b) passed through the Panama Canal or even over dry land, which would be both uncomfortable for him (he's supposedly a sea-dwelling animal, after all) and also would've resulted in him being seen by a lot more people, not to mention a lot sooner.