Long Beach is change from block to block I'm sure you've noticed.
90803,90802,90808,90807 are a few good zip codes but the MLS listings are separated by areas so it can be a little confusing but you want to look in bixby knolls, california height, lakewood village (which is technically still lb), naples, belmont shores, south of conant, el dorado park and park estates are the better areas.
Furthermore aside from looking for the area. Have you been pre-approved yet? A lot of clients have better luck looking for property at your max price and then canceling out the higher end areas like naples or park estates.
If you have more questions pls feel free to contact me I can help you. I was born and raised in Long Beach and I'm a full time Realtor.
Keller Williams Realty Coastal Properties
6621 E. Pacific Coast Hwy Suite 150
Long Beach CA 90803
Cell: 562 279 4979
Office: 562 961 1400
Fax: 562 961 1401
DRE License: 01806412