You must be from California. No one out here calls it "the I-80", or "the 80", its just "I-80". Now, you're on point as to your closest river to the interstate being the North Platte. This site
will tell you your access points south of I-80, but I'm thinking you would rather drive north of I-80 to the Miracle Mile
If you were expecting to be able to fish within 10 miles of the interstate, I don't think you will find much luck.