Holden Arboretum is beautiful, well thought out and well designed. I went with a group and we hiked/walked about 4 miles on a Saturday.
There's a variety of trails with differing difficulties and features. Some out in the open and some under tree cover (if you want to avoid the sun). Whether you just want to amble through the gardens and park your butt on a bench in front of a pond, or you want a sweat inducing hike through streams and steep slopes (see: Stebbins Gulch), they offer something for everyone.
Plenty of ponds and streams. There is a lot of (unobtrusive) signage throughout so you can identify the species of trees and flowers. They offer classes and a variety of events for all ages.
With the exception of a few designated areas, you can take your pooch along with you (if you're cool with stopping every 15 feet so they can pee on things, of course).
Holden Arboretum is a 45 drive from my home, so it's not somewhere I'd visit regularly, but I would love to return in each the spring, summer and fall. A great place for photographers as there's so many different vistas.
Be prepared to pay for your ticket(s) at the gate while you're still in your vehicle (before you park).
Holden Arboretum is lovely and peaceful. I think (most) kids would enjoy it as well. Definitely worth checking out!