Pros
Near the center of power; lots of glitz and talented people. Great networking environment combined with an opportunity to make a difference in the world. Excellent pay, especially if you're a good fundraiser for your program. Neither a liberal nor conservative think tank, nor one that is primarily corporate or labor dominated.
Cons
Not a good place to work if you're a serious researcher. If you're on the fellow/journalistic side of the foundation, you get a fair bit of independence, especially if you've got a high profile byline. If you're on the program side, expect to toe the line of your program, its fundraisers, and its political allies; in other words, work on the program side has a lot in common with work at an advocacy group in DC. At New America, it's usually not necessary to tow an ideological line such as at Heritage (conservative/Republican) or Center for American Progress (liberal/Democratic). But there are plenty of other lines to tow that an academic should feel uncomfortable with.