Double majoring History with something else is definitely very manageable. As for the department itself, I'm not all that familiar with it. I knew a couple people who were history majors and they seemed to enjoy it. I think one of the courses I took cross-listed with the history department and it was very good. I have no idea what would define a "strong" history department. You'll have to do the work and compare the schools yourself (unless someone else posts a detailed reply).
To me what I would care about in a history department is whether or not there was a wide variety of courses offered that interested me and if the professors can teach well. The first criteria is easy to research at any college history department's website/course catalog. The second can't really be researched. Sites like RateMyProfessor.com have so few reviews for most professors, that they probably don't give an accurate picture.
What would be great about doing history at Cornell (in my opinion) isn't necessarily the department itself but the opportunities the university as a whole affords. If you wanted to supplement your history degree with language study, or double major in Economics (something more marketable for a job), or take a Middle Eastern literature course, Cornell offers more than most. Then of course there are all the non-academic factors that go into the college experience as well.