Kepler's Books in Menlo Park, Day One in Palo Alto (in a cute little mall), Stanford Shopping Center, Libraries, Target or Babies R Us, Red Rock Coffee in Mountain View (you'd have to change baby on the carpeted floor, but you wouldn't be the first).... In terms of restaurants, I think it would be fine to call a place to ask if they have a changing station there (what a great way to advocate for them even if they don't!)
I can totally relate to wanting to feel confident you can take care of your little one when you go out. I felt pretty trapped when my 7 month old was a newborn. Here's some things that helped open up my world a bit:
-Keep errands/excursions pretty short, but do get out of the house. Some of my most frustrating experiences have been lining up a series of things to do and winding up with an unhappy kid halfway through my list
-Breastfeeding in the car or in a dressing room is a handy go-to prior to when you feel generally comfortable feeding in public. For me, a nursing cape and a strategic wardrobe (loose bottomed shirts, a scarf) helped me build up the skills and confidence to now feed anywhere and everywhere :) I've also enjoyed La Leche League meetings as a way to get out of the house and also to learn more about breastfeeding
-If you change your baby right before your errand/excursion, you really might not need to do so again for a spell. I know it sounds funky, but the back seat or (in a hatchback) trunk of the car works well. Again, dressing rooms can be handy here.
Hope you get a bunch of replies and Congratulations!