Running and/or Walking Events: Hi-Tek Racing: Lists running events, yes you can walk too, in the local area and throughout Connecticut.

Parks

City of Danbury Parks. Danbury has several parks, of which two in particular are great for hiking: Tarrywile Park and Bear Mountain Reservation. 

• Tarrywile Park: 717 acre park with hiking trails and lots of natural settings. Google Maps, Southern Boulevard
• Bear Mountain Reservation: 140 acres of mostly undeveloped, passive recreation with conservational outlook, ranger cottage and parking area Google Maps, Bear Mountain Road

Connecticut State Parks Several state parks good for hiking. 

• Squantz Pond and Pootatuck State Forest: the two parks are located adjacently in New Fairfield, great views of Lake Candlewood. Access to Pootatuck is through Squantz. Google Map
• Huntington Park: Hiking, mountain biking; NOTE: Hunting (archery) September through December. Located in Bethel, Redding, and Easton. Google Map
• Macedonia State Park: The Blue Trail crosses Cobble Mountain and several other peaks, offering outstanding views of the Catskills and Taconics. 2,300 acres. Google Map.