1st tome home buyer in LA

Hi All. Need some suggestions from the experienced person. Me and my wife both work in UCLA and we are planning to buy our 1st home in next few months. Currently we are only going through the zillow and looking at homes. We have two kids 7 and 4 and we are looking at homes with good schools. However if schools are good all the houses are too expensive. We make combined annual of 180k and we have 220k cash savings. We are planning to do a down payment of $150k. We are to compromise our lifestyle if we can get a home with good schools for kids. Any suggestions which neighborhoods we should look and upto what price? Renting is becoming expensive slowly so dont want to rent anymore. Currently paying 3800.

Edits: Thank you everyone for your suggestions. We talk to our bank two months back and they said we can get upto $1,115,000 mortgage. However at that time I didn’t proceed as I was negotiating another job in a different city. But our current employer ready to give advancement and we should be making ~$220k by this year end. However I dont want to consider that until and unless it starts coming to our hand. So currently I think we can afford upto $850k. But in practical will it be feasible; honestly I dont know.