There are two relatively new blasted rock tunnels along Highway 61 north of Two Harbors. The first one you approach heading north, has a turnoff where you can park after exiting the tunnel and you can walk up a ramp and up around the outside of the rock tunnel.
You'll want to have a car when visiting Northern Minnesota. Technically, it's possible to take a bus or a train, but you will be very limited in terms of where the bus or train will stop and this will limit your freedom of mobility.
Hiway 61 is the only road up the north shore, you can try to bike it but there are alot of cars on the road and it can get pretty narrow.
The traffic can get awfully thick especially on weekends. But it is a very scenic drive, I suggest taking the scenic route from Duluth to Two harbors at least once, it is a lot slower than the expressway but worth it.