Hawkeye gives you some good insights to help you along. You should first understand that it a violation for licensed agents to discuss demographics, crime statistics, and school rankings.
With that in mind, it is always best to utilize the tools available online to research various neighborhoods and cities. I always like to Google the Police and Sheriffs departments for crime statistics and updates. You can also search Google for city demographics as well. http://www.Greatschools.net is a great website, among others, to research data for schools and school districts.
Both Redfin and @listings (http://www.atlistings.com) are Brokerages that offer 50% rebates to buyers as company policy. Redfin is more hands off with buyers whereas @listings performs the exact same services you would find from any Full Service, Boutique Broker. I would check both out as they can offer great savings to Buyers.
Absolutely. Check the crime stats on San Mateo, here:
Basically anything Green, Orange, or Purple is okay. Yellow, especially East of 101 is very much not okay. Blue is marginal, gets better as you get closer to Belmont.
A good rule of thumb when looking at San Mateo, Belmont, and San Carlos is that as you go West from HWY 101 and up into the hills, things get better. The narrow strip between 101 and El Camino Real is usually "lower end" and things get progressively nicer as you move West of El Camino Real.
I know these areas very well and have been shopping for homes there for almost two years. I'm not a realtor, just a buyer with a young family, just like you.
Also check out http://www.redfin.com, which has free access to the MLS data, plus demographics, trends, school ratings, etc., etc. Note that if you use Redfin to buy a house, they'll rebate 1.5% of the buyers agent commission to you in cash (you can use it for closing costs or just take a check). They also have great forums with a lot of very helpful posts and NO realtor ads. Sometimes on Trulia you don't actually get any info, just 100 Realtors saying "best to have an agent, call me dearie".
Good luck and let me know if you have more questions about San Mateo / Belmont area. Sorry, can't speak to Mountain View.