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 that you can go inside.
The park is gorgeous, child and dog friendly, and just plain fun. I recommend visiting in April or May, when the flowers are blooming.