LAX; Marina Del Rey & Culver City to the N of LAX are going to be fairly pricey, same thing for El Segundo & the beach cities S of the airport. Inglewood, Westmont, Florence, South Gate, Lynwood & Compton are rough hoods. You'll prolly find decent deals with the shortest commutes in Hawthorne & Lawndale. Torrance & Carson can get to be a hike depending on time of day but will likely have decent deals. If commute time & particularly distance isn't so much a concern, then in order of preference based on clean & quiet neighborhoods would be; Norwalk, Cerritos, Paramount, Bellflower, Lakewood, Signal Hill & then eastern or southern parts of Long Beach.
Sorry I'm unable to quote prices since my wife & I own our place & haven't been in the market. If you've got time check the classifieds at www.ptconnect.com -Long Beach paper, & www.latimes.com
BUR; mixed bag, that. All the neighborhoods up there are mixed and matched together; one good one next to a not-so-hot one; Glendale seems to be fairly consistant regarding decency.
ONT; Ontario is wide open; haven't seen a bas neighborhood there as long as it isn't next to an industrial/warehouse area. Upland and Claremont seem decent; I'd shy away from Rancho Cucamonga or Fontana.