The Mississippi is big water and a hike across the state for you as it forms our western boundary. Depending on where you put in different regs may apply; Iowa/WI or MN/WI boundary regs can be a little different and to fish too far on the "other side" will require a license from that state. Not trying to steer away as there are lots of opportunities just want you to be wise if you decide that's your destination.
The Wisconsin is another choice (already mentioned) and has a healthy walleye fishery. There's also a couple wide spots that function somewhat like lakes (well sort of), Petenwell and Castle Rock.
You can run the Wolf River from Poygan (near Oshkosh) clear to Shawano before you encounter a dam. In the spring it gets pretty busy with walleye and white bass fishermen until the general opener spreads 'em out a bit. Just north of Shawano is Menominee County which is Reservation land. Again, different rules and culture. As you go farther north on the Wolf it gets more remote and still offers a lot.
You could head north of Green Bay and hit either the Peshtigo or Menominee Rivers. The Peshtigo is closer and has at least a couple of campgrounds I believe plus a number of flowages created by power dams and is known for smallies and walleye as is the Menominee. The latter (not on reservation land) is the NE boundary of of WI/MI and flows south (in WI) from about Iron Mountain and empties into Green Bay as does the Peshtigo.
The south part of the state has the Fox upstream from Green Bay. Not much like a river right away until you get out the west end of Poygan, then you'll run into a couple of dams that make Puckaway and Buffalo lakes. After that I think it's clear sailing to near Portage, not certain about the navigability of all of that though there's at least two more natural lakes it flows through. The Rock starts up around Horicon Marsh, flows south joining the Crawfish at Jefferson and continues south through IL until it meets the Mississippi at the Quad Cities area.
Plenty of opportunities. Good to look ahead and make plans. Should be a good trip!