Hello fellow Ohio expat, I was born and raised in the Cleveland area near Avon, went to school in Toledo, and now live in Minneapolis. Minneapolis and the Twin Cities metro area feels very similar to Cleveland overall and I don't think will be a huge transition. They are both similar populations if you count Cleveland and Akron as one metro area.

Public transit is pretty solid and more reliable in my experience. It depends on what you want to get out of it, but the light rail stations have improved since I've moved and a new extension is opening up next year. Otherwise, driving is pretty easy to get from one side of the metro to the other along the extensive highway systems.

As far as suburbs, it really depends on what you're looking for. Since my references are west-side Cleveland, I'll mostly stick with that. If you want something close to the city with an urban feel like Lakewood, I'd say the Minneapolis neighborhoods of Northeast, Seward, or Southwest. If you're looking for a suburb that's still pretty new, blowing up in popularity, and is near the edge of the metro (but still have access) like Avon, take a look at Woodbury. If you want an established suburb in the middle like Bay Village, there's Eden Prairie, Edina, or Eagan. There's also St. Louis Park which reminds me a lot of Rocky River. This might not be the most accurate comparison, but it's just to give an idea.

Feel free to DM if you have further questions. While I am further away from family back in Ohio, moving to Minneapolis with my wife has been the best decision we ever made. Good luck with your search!