Contrary to popular belief, Raleigh Peak Road is an excellent route to reach Raleigh Peak from the east. While it is used to access the single dwelling NW of the peak proper, it is completely on FS property and is open to the public.
Having said that, if you park at the junction of CR 126 and Raleigh Peak Road, don't block the gate! It is someone's driveway and common courtesy says you shouldn't block them in or out.
Basically the route follows the road, the Colorado Trail or a combination of both. The most straightforward approach would be to just follow the road until you are almost due north of Raleigh Peak, then follow the North Face route.
Just north of the Buffalo Creek Fire Station you will see a gated road on the east side of CR 126. This is Raleigh Peak Road.
This is a hard packed dirt road that traverses an open ridgetop. Its easy to follow, hard to miss.
It's about 4 miles out to the point where you need to leave the road to head for the peak. A mountain bike would make the trip much faster.
Boots or bike.