Yes! I started as an intern with the federal government when I was 19. My boss there talked me into opening a TSP account (basically a 401K). By the time I was graduating, I had already saved a little for retirement. And with compounding interest, saving $100 now is so much better off in the long run than waiting 5 years to save $100. Even if you saved no other amount.
I've become obsessed with saving for retirement. I've had that 401K since I was 19 that I've rolled over into every new job I've gotten and tried to contribute the most I can, and I have a Roth IRA. Plus 401K contributions aren't taxed! If you're in the 25% tax bracket, for example, $100 into your retirement is only $75 you'd get in your pay check.
Anyway,
@Eyes On The Prize, if you have any questions I know all about all of those accounts. 401K, 403b, Roth vs. Traditional IRA, etc.
Boston is great! If you live in the city you won't need a car, but it's expensive. And you'll be limiting yourself if you can only au pair in the city where you won't need a car. The city of Boston itself if small and the Boston area is a lot bigger, but public transportation itself isn't that great outside of Boston proper.