Just got back from vacation. 3 days in San Francisco 1 day in Monterrey Coast drive down the Pacific Coast Highway 3 days in Los Angeles Beautiful things to see along the way, for sure.
You need more than a day but there's so much to see up here. Minneapolis itself has hands down the best urban parks system in the US. I was just floored when I moved here and saw how great the parks were in the city. But you can drive 2 or 3 hours north to Lake Superior (either along the north shore in Minnesota or you can go east along the shore through Wisconsin) and just find some incredible sights. There are several small towns along Lake Superior in Minnesota or Wisconsin where you can get a room at a bed and breakfast or a small hotel. You can also go North to the boundary waters near Canada and just get a canoe and ride through of the lakes and rivers up there and go camping. If you're into fishing, I know a lot of people who tell me that the best fishing is actually on the Canadian side of Lake Superior which is about a 5-6 hour drive from Minneapolis. If you just want to relax, you can also rent cabins or lake houses in central and western Minnesota on some of the larger lakes. People here in Minnesota are big on the outdoors. And since we only get a few months of the year where it isn't crazy cold, people take advantage of the natural beauty here. As someone who moved here relatively recently from Texas, I can't even emphasize enough how awesome the outdoors are here in the Summer. Unfortunately the winters are truly miserable at times but its still a great place to visit.
Whataburger, and it's not close. Not even a little bit close. In-N-Out is a nice little hamburger. But it's nowhere near Whataburger. I'm surprised people even entertain the notion.
Would and have. If you like camping and hiking it is incredible. Even just driving along the cost you see some incredible stuff and if you don't like to hike there are some decent resorts along the coast.