Welcome aboard! First off, just so you don't get any crazy ideas, there are NO muskies in the Chippewa R!!
The landing you'll want to use is on the north side of the river right on the bend where Water St turns in Menomonie St. Right near Hobbs ice rink. Pretty easy to get up to the hole where Little Niagara runs in. Gets tricky going up further to either where the Eau Claire R meets or below the rapids at the city shops. Go slow and have a spotter up front til you figure it out.
Going downstream is a bit easier. If you have a small boat and 4wheel drive you can put in underneath where I-94 crosses, north side of the river also.
Shore fishing is always an option, but you usually do better in a boat.
Hope this helps, fire away with any more questions.
Ah, I remember my UW-EC days!!