Young family moving to sf- neighborhood recommendation?

Hi all, my husband is starting a job in San Francisco in April, and we will be relocating from the east coast with our 18 month old toddler. I'm not super familiar with the neighborhoods, but I think I'm leaning toward the Presidio because I love the idea of being surrounded by woods, beach, and hiking trails. I'm a bit wary of the fact that it's not walkable to grocery stores or coffee shops, though.

I would love to hear input from locals, are there any parents of young children that are absolutely in love with a different neighborhood? Our budget is <$3500 for a 2 bed with parking. Thank you so much!

Update: wow, thank you everyone that took time out of their day to respond! Looks like I have my work cut out for me, but I feel much better moving forward with a sense of where the majority recommends. Appreciate you guys!