here are a few that come to mind off hand:
Cam Jansen series -- the Scholastic Book Wizard says the reading level for most of these is grades 2-3, and they're not scary.
The Ramona series is a bit harder (grades 3-4 level).
The American Girl books are around grade 4 reading level, but you might consider those a little later.
You might ask a children's librarian at your local library for more suggestions. Ours were helpful and didn't get weird about it if I told them my kindergartener was looking for books at reading level X.
