As a current resident of Los Angeles for more than 2 decades, this is my opinion:
1.You need A LOT of money to LIVE in LA. If your wife is not planning to work, forget about coming. If you own a house wherever you are and sell it, you will probably be able to buy a garage over here. (I guess that depends where you are now.)
2.Mesivta of Greater Los Angeles – otherwise known as the CALABASAS YESHIVA is an excellant mosad. It is WELL ESTABLISHED and produces wonderful bochurim. I have first hand experience! Rabbi Gottesman and all the rabbeim are superb!! (and if you meant tuition when you said expensive – it is no more expensive than anywhere else. The housing in Calabasas is expensive but I guarantee that is not where you would be living.)Furthermore, unlike all the other LA yeshivos,it is out of the city and away from the pritzus and distractions. The boys stay there all week and come home for shabbos. That has the benefits of both an in and out of town yeshiva. You wont see Calabasas boys between sedarim, reading the LA times from a newspaper stand.
3.Bais Yaakov is excellant! I can attest to that first hand too.
4.Mybat: The pritzus is geferlach compared to other places. Maybe you keep your eyes closed wherever you go. A friend from Miami(where the weather is similar) with family here says that LA is definitely worse!
5.If you are planning such a major family move, I would do a lot of personal research before moving. You will get many opinions about the schools, shuls, and other establishments here but unless you see them yourself, you cannot be sure what is “for you”.