I second Gov2School. I'm only a year and a half out of undergrad at the moment, but I have such a clearer idea of what I want to do. I did apply right out from undergrad, and got accepted to a bunch of places, and later backed out to go work for a year in NYC, and then DC. It really opens up possibilities and it makes you a more viable candidate because you have a clear idea of what you want to do, and the experience to back it up. In my opinion, that all translates very well in statements of purpose and in your resume.
Most, if not all, grad schools tend to look very favorably upon professional experience. It's definitely possible to get in straight from undergrad, but it's also much harder. All of the info sessions and opportunities I had to speak with students all reinforced that SAIS values professional experience, and I don't think I would have gotten in without it. I didn't even bother applying to it straight from undergrad. I do think it would be good to get work first, if possible. But at the end of the day, you're the only one who knows what would be a good fit for you.