paulj is correct, there is no formal river road north along the St. Croix River. If you take 21 north from Prescot to Afton and then pick up 18 to us 95, continue north to US 8, near Taylors Falls, this route pretty much follows the St. Croix River. It's been 20+ years since I was on these roads,so I don't know what condition they are in. There 1 state park between Prescott and Afton. 95 from Stillwater is a 2 lane, hilly and heavily traveled road. Also 2 state parks between Stillwater and Taylors Falls. Long down hill grade right after 95 ties into 8.
I would strongly advise against crossing the river at Stillwater. The bridge is very old and is in pretty poor condition. I can drive over almost any bridge, but I refuse to use this one due to its condition.
After you cross the river at Taylors Falls, there is a long hill, not sure of the grade, but 8/95 is a truckers route, so the grade isn't extreme. About 5 miles after crossing you can turn north on WI 35, which is sort of close to the St. Croix. The river turns east at Danbury and as far as I know, the roads don't follow it to its headwaters. You can stay on 35 all the way to Superior, WI.
From Superior, take US 2 east, to Ashland, which has a nice cg right on the lake or you can take WI 13 east thru Port Wing, Herbster, Corncopia, Red Cliff and then Bayfield. Several county cg's on this route, also at Red Cliff. You can get a boat tour of the islands at Sand Point, or go into Bayfield to check out the Visitor's center, book tours and sailboat trips, take the ferry over to Madeline Island. Sand Point has a visitor's center and is used by most of the kayakers that want to visit the caves between Cornucopia and Sand Point.
Plan on lots of time for this trip, the majority of the roads are scenic 2 lane, hill and curves, deer and wild turkeys, maybe a bear or two and traffic. I would suggest you plan your route and make reservations for cg around Lake Superior soon. The Apostle Islands are very popular and cg's can be full, especially at holidays.
Enjoy, Judy