So you’d be putting $55k down, and financing $495k if you stay at $550k house.
The $65k you have liquid will be eaten up entirely by the purchase if you put 10% down. $55k for the down, and $10k for various closing expenses and the inevitable trips to home depot once you purchase.
In an ideal world I’d try to figure out a way to stay with financing at $417k or less. I know that’s very hard to do in San Diego. Maybe impossible in your timeframe.
Your income is good… What is your job stability? Are you working in areas that are grant based – where funding could go away? (I’ve got friends who are both PhDs – and one or the other is always scrambling for the next gig when the grant runs out.)
Since you have good income, but less cash… I’d look at areas that are lower cost. I’d rule out most of north county coastal and Carmel Valley. I’d consider larger townhomes even though that may feel less than optimal… you can sometimes get more bang for your buck in attached homes vs detached. I’d look for good pockets in more blue collar areas… Showing my bias towards central San Diego here – I’d be looking in Clairemont, Tierrasanta, PQ, Allied Gardens/Del Cerro, and Poway. Schools are important – but parental involvement is MORE important in the outcome of a kids academic journey.