M.,
I am the mom of a 17 month old daughter and we live on the east side also. And I recently switched jobs to go from 40 hours a week to 24 hours a week with every Friday off. So I may be interested in a Friday option.
Are you aware of some of the options that already exist locally? My first Friday off we went to open gym time at Water's Edge Gymnastic... it's $5 and is from 10 to 10:45am. This past Friday we met a couple other moms and babes (19 and 20 months) at East Bay Park at 10am...after 2 hours on the beach we had a picnic lunch on the grass, and headed home for naps.
I work on Wednesdays, but there is a play group at MCHC for toddlers from 10:30am to 12pm. You may want to try it...it's a great place to connect with other moms to start another play group. That play group is year round, but there are other playgroups through TCAPS that run through the school year.