Pros
AEI was a good place to be a research assistant for a couple of years. I learned a lot about Washington, both from the work that I was doing and from being around the kind of insider-y people who I got to meet. I got to do a lot of research and writing. People were basically friendly. You'll eat lunch with senior staff members. Because there are so many young people working as research assistants, it's easy to make friends. People are in general very bright and reasonably competent. You can disagree with the ideology, at least as a research assistant, and no one's going to ostracize you.
Cons
There's very little training either for assistants or for the people managing us. Very little in the way of performance reviews. Whether you get significant feedback on your work depends strongly on who you happen to be working for. People are very proprietary about their areas of expertise, both on the research and non-research side. Assistants aren't fully utilized intellectually, and there are some rote tasks that I feel like assistants do because no one ever thought through whether there was a better way to do them. The ideology is strong, which can be a great learning experience, but if you want to write things for AEI, especially as a junior person, there's a company line.