The size of New York's Central Park: 843 acres. Not too shabby, but Fairmount Park in Philadelphia is comprised of 9,200 acres. Win!
Fairmont Park is the nation's largest urban wilderness, and home to 57 miles of trails, from off-road to paved sidewalks, and 160 natural springs. It links 9,000+ acres of rivers, creeks and waterfalls in the area. The 25-mile Schuylkill River Trail actually runs from downtown Philadelphia to Oaks in Montgomery County. (In Pennsylvania, not Maryland. It's not that long.)
Don't worry about too much overcrowding for the picnic you'll have planned -- there are 139 picnic sites available. The Grove, a gated picnic area, has two picnic pavilions, water/electric hook-ups and grills.
The park also has a disc golf course, horseback riding and rowing, plus several museums, if you like some indoor fun with your outdoor fun. The Mann Center has a full calendar of notable acts -- from indie rock to classical -- and offers plenty of moonlit concerts to partake in.