See, you did it all wrong. You’re graduating from your hometown – very bad decision. You should have made your first cross-country move upon entering college. ( )
To actually answer your question (sort of): I’d have to say it all depends. What’s your degree in – do you expect to be making a fair amount of money? If Boston was mentioned seriously, and not merely as a random example, are there lots of opportunities there in your field?
Depending on how bad you want to move to Boston (or wherever) you might do both – look for jobs there first, but be prepared to move there jobless. Again, it depends – how much money do you have? What living standards are you prepared to accept in your destination city? If you want to get out of town that badly, you could probably survive nicely for a while in a room at the Boston YMCA, and go ahead and move with just a small savings. If you really require a waterfront view, depending on your bank account, you’ll need a good job first.
To pick a new city, you ought to visit first. I visited Seattle four times, in different seasons, before I become set on moving there. Still, if a particular city attracts you because of its opportunities or some other special reason, you needn’t visit – you’d survive anywhere for a while, and then you could move again if you hated it that much. I’ve lived all over the country, and it’s kind of fun in its way.