If it’s a sunny and warm weekend afternoon, you can count on there being a crowd lazing around the large grassy expanse that is Yoyogi-kōen (代々木公園), Tokyo's most popular public park. It might be a bit tatty compared to the city’s more manicured gardens (and overrun with crows), but that's only because it gets so much use.
This is where locals come to jog, walk their dogs and teach their kids how to ride bikes. It's an excellent place for a picnic and probably the only place in the city where you can reasonably toss a Frisbee without fear of hitting someone.
Across the road (use the overpass), there's a concrete plaza where events are held most weekends, especially during the warmer months. These include festivals celebrating the cultures and cuisines of Tokyo’s foreign communities. Whatever’s on, you can count on there being yatai (food stalls) and crowds of revelers.