I write on my blog http://www.frontdoorblog.com about Burlingame neighborhoods all the time and should probably focus on these two neighborhoods more. Lyon-Hoag is close to Washington Park, Washington School, the train station but potentially also closer to 101 and you might compromise on traffic noise. Burlingame Terrace is in good walking distance to the shops and restaurants on Broadway, andMc Kinley Elementary School. Every neighborhood has a different feel and it depends what kind of house at which price point you are looking.I live and work in Burlingame. Let me know if I can anser specific questions.
You might want to check out BurlingameBuzz.com for more information about the Burlingame community. I've also pasted a link below to a google map which has general information about all the neighborhoods in Burlingame.
What particular information are you interested in for the Terrace and Lyon-Hoag? Having been born and raised in Burlingame, perhaps I can point you in the right direction.