All great answers below. Additional thoughts/details
From the "village" walk-able area I would recommend Willow Glen (95125). If you choose a home in the Booksin school area, you are covered with a good school up until 5th grade. Willow Glen offers ranch or newer custom homes in your price range all within walking distance to downtown. Great sense of community. Events throughout the year. . The other advantages of Willow Glen, quick to the highway, CAL TRAIN, light rail and airport.
Check out the local web sites of to get a feel for the local goings on
Cambrian Park great area but not as walkable. Tends to have larger lots, but the main draw is the Union School District. K-12 - great schools. Architecture is more ranch/suburbia, not quite as unique as Willow Glen. No "hub" of shopping/restaurants other than strip malls/chains. Quick access to 85/17. The main pull is schools.
Campbell - great downtown, best market on Sundays (imho). Restaurants, nightlife, near the Los Gatos Creek trail that you can ride/walk to Willow Glen or Los Gatos. Schools, not so good, and Campbell struggles with having good street "pockets" surrounded by rentals. This is fast becoming the most desirable place for young couples that do not yet have school aged kids.
Los Gatos certainly can offer the downtown walkable attributes. Great market, more choices for dining, great schools. Less house for your money. One way in and out - HWY 17. You still have access to Los Gatos Creek Trail and much more shopping/dining than the smaller communities.
Mountain View - All of the above simply more pricey. Depending on the commute desire Mountain View may be more desirable than more South Bay neighborhoods. Mountain View is known for good schools. Check out the boundaries carefully.
Another ares to mention is West San Jose (95117) Near Santana Row. Look for Moreland school district and you can find good schools. Santana Row is the draw. Not extremely walk-able otherwise. Advantage, easy on/off to 280. Quick to Sunnyvale/Santa Clara/Mountain View for high tech commute.
Cambrian is most likely going to offer you the largest lots, but Willow Glen has some as well.
Mountain View and Los Gatos, less lot, less house for the money.
Check out http://www.schoolperformancemaps.com
to get a better feel for where good schools are and how they relate to the neighborhood. I have a soft spot for Willow Glen as it is my own neighborhood. I chose it for a some of the same reasons you mention in your question. It will be important to go over all of your priorities to really fine tune the criteria so your agent can help you find the best neighborhood.