So to answer your question (not in regards to academic reputation, b/c all Ivy league schools could do that).

-Yale (the other notably liberal Ivy)

-Hampshire college (just like at Brown you can get course performance reports instead of grades)

-UCSC, used to have a grading system like Brown, and is strong in the humanities and biology, too, so it attracts a similar range of students.

-Reed

-A lot of people would say Berkeley, b/c it is academically strong and has a liberal rep, but I think it is too huge and has too much of an off-campus life to really be too similar to Brown (my best friend from high school went to Berkeley, and I spent a lot of time there); also being a public school, it doesn’t care about you in the same way, and grades much more heartlessly.

If you pose a more specific question regarding a particular attribute about Brown, I’d be glad to answer more. I think the “liberal learning” mindset of Brown is what shapes it most because it allows students to relax a bit more, although it remains an academically competitive environment (largely b/c when you don’t have +’s and -‘s your peers don’t feel like they are in such a tight competition with you for grades–something I definitely felt at Columbia and Cornell).