US News puts out a report every year on the best colleges for various degrees. Here's a link to the best undergrad engineering schools.
http://colleges.usnews.rankingsandreviews.com/best-colleges/rankings/engineering
And here's the complete listings just for best ME schools..
http://colleges.usnews.rankingsandreviews.com/best-colleges/rankings/engineering
There are other ranking reports out there, although US News is one of the more popular. Still, rankings aren't everything. I'd happily put my aerospace degree from UCLA up against one from Stanford or Cal (since I know folks that went to both of those schools), but they show up on the lists and UCLA doesn't.
Still, if you look at all the engineering lists it'll give you a pretty good idea of what schools value the major, and you'll notice that the better schools don't just show up on the mechanical list, or civil list, or aero list, they show up on ALL of them. MIT for example is #1 on about half of the specialty lists, which makes sense as its pretty much the highest regarded school for math, engineering, etc.
I think the more important part is that you actually LIKE the school you're going to, so it pays to visit a few schools. Actually walk around and talk to people, or even better, talk to the professors, academic advisors, etc to get an idea if the school matches up with what you want to do. Because if you don't like the school, or the department, professors, etc, its going to be a lot harder to finish. And unless you're really looking at the top couple of percent of jobs out there, a degree from most engineering schools is going to get you where you need to go, as long as you finish it. I know plenty of guys that went to schools that are no where on that list that have
very nice careers in the industry.