Patapsco Valley State Park winds around the western edge of Baltimore County, including parts of Howard and Carroll Counties and has a huge range of outdoor activities for any level of fitness or interest. The closest entrance to me is in Catonsville itself--there's a great tire park/playground that is a popular spot for birthdays, school trips, or just families having fun. It's ringed by picnic tables and fairly decent bathrooms so you can make a day of it. There are hiking trails off of this area; my favorite goes down into the valley and joins up with a longer and wider trail that parallels the Patapsco River. It's a short and easy hike, so it's perfect for families with young children. Walk a little ways along the river trail and you'll get to a swinging bridge that I think is nerve-wracking to go over, but my family loves it.
Other entrances to the park give you access to activities like mountain biking and road biking, equestrian trails, tubing and canoeing, and fishing. There are camping spots throughout the park (including a few at the Catonsville entrance) as well.