Probaby a bit far, but:

Pleasanton Golf Center has grass range, no woods though and a par 3 course. This is in the middle of the Pleasanton Fairgrounds horse track.

Out in Sunol (souths side of the freeway) as you are going to the Sunol Golf Course there is a driving range that has grass.

The Bridges in San Ramon used to let us hit from the Grass (and does the week that the LPGA is in town) and has a good deal on the range. You can buy $150 worth of balls on a rang card for $100. So to start you get a 20% discount!