From the WI side, you won't pick up the GRR until the Prescott/Hastings area. North of Hastings, the Mississippi is fully inside MN. Prescott/Hastings is where the St. Croix River empties into to Mississippi and the Mississippi becomes the state border.
Detailed map of the Great River Road, really interesting to see, use the size increase function in this PDF to get close details:
St. Croix Falls (the starting point you mentioned) is in WI, across the St. Croix River from Taylors Falls, MN, on WI 35. This point is, oh, about 50 miles as the crow flies north of Prescott/Hastings.
I've been on both WI 35 from Prescott to the Illinois border (down to Galena, IL, actually) and US Hwy 61 on the west side of the Miss in MN, both are beautiful. Hwy 61 probably carries more traffic, and has more sections of 4-lane. WI 35 is 2-lane, quieter, has more enjoyable wiggles, and passes through all kinds of neat little towns.
When returning from Galena to Minneapolis, we jumped the river at Dubuque, Iowa, and skirted the river north on a mix of county roads and 2-lane highways. Holy smokes, that was downright delicious! And we were in the car. I gotta get back there on my bike.
As to the entire length of WI Hwy 35, I've ridden its entire length from Superior, WI (across the harbor from Duluth, MN) to the Illinois border. As far as I'm concerned, the stretch from Prescott, WI south to Illinois is wonderful. North of Prescott to Superior is no big deal at all.
Enjoy your trip! Get an extra memory card for your camera.