There are a number of outdoor recreation areas near Baytree where residents can go to enjoy vigorous activity in the fresh air.  Most are within walking distance.  This list by no means complete:

University Terrace Park  (.2 miles)
A playground for children, basketball and tennis courts, a large grass field and an off-leash area for dogs.

Westlake Park  (.3 miles)
Big duck pond with a small playground, benches, ducks, geese and the occasional swan.

Pogonip  (.8 miles)
Open space and trails for hiking, horseback riding and cycling, and offering beautiful views of Santa Cruz and the Monterey Bay.

Moore Creek  (.9 miles)
Undeveloped greenbelt reserve open to day hiking only.

The UC Santa Cruz campus  (.3 miles - Entrance[Bus,Shuttle], 1.44 miles - PAF West, 1.52 miles - PAF East)
(Enrollment or Membership required) Fieldhouse facilities, court sports, swimming pools, hiking and bicycle trails, etc.

Distances shown are straight line (as the crow flies) approximations using Google Earth