Michinoku Park, located an hour west of Sendai, is a great place to spend the day. With its beautiful scenery, landscaping, and lake, there is plenty of nature. There are also a few big play areas for children. The park is a great place to have a picnic, go boating, or just relax. There is also an area with historical homes from Tohoku inside which you can go.
The opening hours vary by season, but are posted on the official website. The admission to the park is 450 yen, and the park can be reached via bus from Sendai Station.
The park is gorgeous, child and dog friendly, and just plain fun. I recommend visiting in April or May, when the flowers are blooming.