Traveling to another city to participate in an event can be quite an experience. It allows you to see the city in a way that most people don't get to experience. At least not the same way YOU are experiencing it. Last year, I ran Big Sur... long story (race recap) short, they close Highway 1 and you are running on the California Coast (or as the slogan says: running on the edge of the western world). Sure, everyone could just drive down Hwy. 1, but to truly appreciate the view, imagine it by foot while running up a 520 foot climb over 2 miles called Hurricane Point. The journey is a reward in itself, with the view as the cherry on top.
If you schedule the race early in the trip, you get a "quick" tour of 26.2 miles of the city, leaving you the remaining time to relax and enjoy your vacation. If you schedule it late in the trip it can serve as the final hoorah before you return home. Both options contain pros/cons, but just remember you are doing two things in one swing: visiting a place you always wanted to and second: running in a place you've always wanted to visit.
And you can't be embarrassed by wearing your finisher's medal the rest of the day in public. After all, they're strangers and you won't see them again... or will you?
Note: My first marathon was in 2006 in the lovely city of Florence, Italy. Training for 6-months was just a little bit easier imagining how beautiful it was going to be... give it a try! It's worth it. I just booked my airfare and hotel for New York in November... although I have been to NY before, it totally counts as a destination race since I live on the other side of the country. Cheers.