First, find Skyline Drive and enjoy the views of the city while you head towards Enger Park and Tower. It's a bit tricky to find - you have to leave Skyline Drive near a pond and small bridge - but you can see the tower up on the bluff. Circle back if you seem to be leaving it behind. Climb the tower, enjoy the gardens, and ring the memorial bell.
Split Rock Lighthouse is nice, but admission is fairly expensive. Instead, drive up to Two Harbors (take the scenic route) and find the lighthouse. You can't tour the lighthouse because it's a bed and breakfast, but you can park for free and walk out on a concrete structure across the water, examine a mini-lighthouse, and soak in the sunshine bouncing off the lake.
If it's a hot day, Gooseberry Falls, north of Duluth, has short-term free parking. Put on your bathing suit (if you don't mind an encounter with a leech) and go to a park that lets you get up and close to the Falls. The Visitor Center is very nice and has a gift shop.
Back in downtown Duluth, drive over the Lift Bridge and watch for a public parking place on your left. Park and take a nice long walk on the beach.
Then go back across the Lift Bridge and end your day at Canal Park, the greatest place ever. Just sit and watch the boats as they approach the Lift Bridge and force it to rise. Watch the gulls circling and hoping to grab a bite off the sidewalk. Walk out on the concrete ramp. Try to skip some rocks off the shoreline. Visit the free Maritime Museum at the foot of the Lift Bridge. Find a great deal on a sweatshirt in the quaint little shops.
Duluth is the closest thing to an ocean you can find in Minnesota, and you don't have to be rich to enjoy it.