It's very unlikely that you will be able to find a suitable place with that salary, unless your wife is also working.
First, it would cost 4-5k for a 2 bedroom in Palo Alto unless you find a willing landlord. Probably 5-6 for a 3 bedroom if each child needs her own space.
Second, I think that would only work if you have a combined 170-200k salary and you may get shocked at the sticker price for childcare and more.
My recommendation is to live in the East Bay across the bridge at Union City or Fremont. 20-35% cut in prices. If you insist on living on the Peninsula, Redwood City is a little bit cheaper than Palo Alto and Foster City can also be quite cheap. The only negative is it's on reclaimed land and there may be safety issues if there is a major earthquake.
Welcome to the Bay!