The Hoover Institution at Stanford University, where I'm now a Senior Fellow, has long offered up-to-5-year paid in-residence positions (with no teaching obligations) in various fields.
This year, we'll also be considering people who are interested in becoming legal academics. We expect the selection process to be highly competitive: The position is unusually generous, compared to other fellowships, in salary ($165K-230K/year plus a $20K housing allowance), potential length, and lack of teaching obligations.
To be realistically eligible, applicants should have clerkships, top grades, published law review articles, and plans for new articles. It seems likely that most applicants will be from the Usual Suspect academic feeder law schools, but I'm a UCLA law graduate myself, so I'm certainly open to top people from other schools as well. We have no particular preferences for any particular fields within law: We'll gladly consider people who want to work in business law, constitutional law, international law, criminal law, immigration law, and all sorts of other topics.