Cheesman Park is the prettiest green space in central Denver — 80 acres of grass, mature trees, and a long view across the city to the Front Range, anchored by a 1908 white marble pavilion that is one of the most photographed structures in town. The neighborhood around it, with its Victorian apartments and Capitol Hill mansions, is one of Denver's best for an aimless walk.
The Denver Botanic Gardens are immediately adjacent on the east side, so combine the two. Sundays in summer fill with picnickers and frisbee games; the rest of the year it's a quiet running loop.