There are a few good dog spots around SOMA including the Mission Creek Dog Park, South Beach Park, and Esprit park. I've put together a google map of all the dog parks which you can layer on to other google maps to get a better idea of the neighborhood. Here is the direct link to the map:
http://maps.google.com/maps/ms?ie=UTF8&hl=en&msa=0&a…

I also have the link to it and some other good SOMA dog resources on my dog blog. http://www.dog2point0.blogspot.com

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

Hi Christine - Though there aren't many green areas for dogs in SOMA/South Beach such as a specific dog park or dog run, the closest are:
1) South Park - Located btwn 2nd 7 3rd/Branan & Bryant
2) The Embarcadero - Lots of concrete with some grass
3) Berry Street - the new buildings have some grass between the buildings and there is a walk way on befind them.
4) Behind Berry Street on the other side of the canal (from 4th street?) - when you are behind the buildings on Berry, you'll notice a grassy area on the other side of the canal by a new building that looks like a coffee shop

I hope this helps. The link below also suggests other parks in other areas.

Hi Christine. There is a green building called Arterra located at 300 Berry. I believe they do allow dogs although there are number and size restrictions.