Hello Josefina. I have lived in Cleveland, New York City and am now in Los Angeles. Cleveland's public transit is efficient to get to most areas in the Greater Cleveland area (city and near suburbs) through a combination of bus and light rail. When you add the ride-share services like Uber and Lyft you will be able to get anywhere without the need for a car. You will need to get used to being outdoors during inclement weather if you need to go somewhere while its raining, snowing or -10 degrees temperature. There are also very walkable and bike-friendly areas like Lakewood a near-west suburb of Cleveland where you do not need to travel far for your necessities and fun activities. There are neighborhoods where you would not want to be taking public transportation or walking late at night such as East Cleveland, Puritas-Longmeade, Clark-Fulton. Contact @skorasaurus on Twitter for info about various neighborhoods in Cleveland. He and his organization have been mapping the area and are all very familiar with public transit, demographics, safety, and public offerings.
I believe Cleveland is better than other areas in the Midwest. It may not be as massive as NYCs public transit offering but it is comparable in access.