I live/work in Fremont (actually have had family in the Fremont area since 1880!).
I also service Alameda, Contra Costa, and Santa Clara Counties. Please review my Trulia Profile/Q&A and contact me offline if you would like to meet to discuss your plans.
I would generally agree with your friend's comment about schools in Fremont vs. San Jose.
Fremont School API Performance can be found here:
Individual school websites can be found here:
Fremont School Attendance Boundary Maps are here:
This year, several of San Jose's school districts earned California's Distinguished Schools award, which means that the overall API for the entire school district has met or exceeded state standards, so while I can say that Warm Springs Area, in particular in Fremont, has a great school district, I think there are plenty of excellent schools here in San Jose and Santa Clara that can meet your needs.
As for using two different agents to find a home, I do find that agents become very "area specific" after a time. I know more about Santa Clara, Cupertino, Sunnyvale, Los Altos, portions of Palo Alto, Los Gatos and San Jose than would my counterpart in Fremont or Alameda. Similarly, someone in Fremont is likely to know more about that town than would I since I do not live there and have not made that my "market." As an agent, you know about homes in areas where you live, work and socialize, and, for many of us here in San Jose, we don't travel far up and down the East Bay or Peninsula. All licensed agents in California may practice in any part of California, so I can also sell homes all over the Bay Area, but I choose to, instead, specialize in the Santa Clara County and this, in my opinion, makes me a better agent for those looking to purchase in our town. There is also the matter of access to the local MLS services. In Santa Clara, we can access the MLS services of Santa Clara to Monterey and up through Napa and Sonoma, but the East Bay's MLS has been locked to the Santa Clara realtors unless we pay for the extra service and join a Board in the East Bay. For many, the extra expense has not had a satisfactory return on the cost, so we stay with the South Bay/Peninsula/SF listing service, so this is a valid reason to find someone in the East Bay to represent you if you wish to purchase a home in Fremont.
As for your price range, however, the $350,000 may not be sufficient to find a home in a good school district in San Jose. Many of the homes listed even now at $350K, are selling for far more than their $350K price. I have a client who is interested in this price range, and he is finding it difficult to find a suitable home even at $400K. Here in Santa Clara, you can access the same MLS listing that any agent can by going to http://www.mlslistings.com. A similar service, however, does not exist in the East Bay, so you will need an agent.
If you find a home that you like here in San Jose and are willing to do the "legwork" to look at the home, then consider using a facilitator to assist you in buying your home. Facilitators cost a fraction of what the "full service" agent is paid, and does all the same work as a full-service agent. Read my blog here at Trulia for more information about facilitators.
Good luck & happy house hunting!
Grace Morioka, SRES, e-Pro
Area Pro Realty