It's an obvious answer, but the drive from Banff/Lake Louise to Jasper along the Icefields Parkway truly is among the most scenic drives in the world. Another option would be a loop from Banff south/west on Highway 93 to Radium Hot Springs, then north through Golden and back east on Highway 1 to Lake Louise. You'd go through three national parks in this case (Banff, Kootenay, and Yoho).

Most of my trips to the area are during ski season though so I'll leave it someone else to detail the best things to do in late summer. Keep in mind that September 4-6 is a holiday weekend in Canada so you will likely want advanced reservations for the start of your trip at least.