Discussion of Kagan's sexuality (I haven't been able to find any reference to her being publicly out) can be found easily via a Google search. Here's one comment from a recent NYT thread:

"Why are people pretending that Elena Kagan is not a lesbian. She’s not out but that does not change her sexual orientation. She has a female partner. This is an open secret at Harvard Law School among students and faculty. I cannot speak for the broader legal community yet, but I’d have to believe her professional colleagues know as much or more than the students and professors she works with. The real irony would be if she did not get the nomination because she is not open, when the conventional wisdom has always been she has tiptoed through life in the closet for the very sake of winning a confirmation."
http://www.towleroad.com/elena-kagan/