There is no full-fledged place to relax with children, only Nalivaiko, and this is a recreation park for the entire population of the city and guests, not individuals.
Under the USSR, it was a paradise. There was a menagerie, rides, a pond with boats. It's just a memory now. We went to the park, to dancing, to the planetarium. They are gradually restoring it.
It's a great option for walking with children. There is a playground nearby. There are enough benches. Fountain. But!, I wouldn't take my child to the rides!