This is pretty basic and well known but you can source links by using SEO quake in Chrome or Firefox. There are a heap of instructional videos out there on how to set it up and use. The key is in the search string. If you P.M. me I will give you a couple I have used that work a treat.

There is no way you can get a backlink from an edu or gov site in its homepage. You can only place a backlink by commenting on blogs or on other pages of a gov or edu backlink.

You can get PR6 homepage links by paying lots for them if you really want but I doubt they would be from edu or gov sites. To get a link on the homepage of one of those sites you have to be very close with someone who has access to the site.