Lots of good greenspace behind the condo's on Berry Street. Though technically leashes are the rule. You can walk with a generally well off-lease trained dog along mission bay creek from 4th street, down behind the Berry Street condos (stopping at what we call "the hump" between 255 berry and park ?something? condos (right at 5th) for a play session), then continue down to the new park under the off-ramps (great on rainy days and/or really sunny if your dog is sensitive.), then onto the fences in dog park just about a block further (may want leash for this last part as is is along the normal sidwalk right next to Berry st).
Other than the little part at the end of Berry, you do all of this without encountering a street.
All in all this area is fantastic for dog owners