If you want a private pool I would recommend an air bnb.
Will you be here over Shabbos?
What area of LA do you want to stay in?
When are you coming- weather is decent. Not 100s but not freezing. It depends on the week. Nights get cold- 30 and 40s so bring a jacket. We tend to layer because by the afternoon my kids shed their jackets at school and are fine in their long sleeved polos.
It's "freezing" by LA standards. Today is 55 and this week the highest will be upper 60s. 60s in LA is much colder than 60s in NY
Find a hotel near Pico/Robertson (those are cross streets) or Beverly Hills area - tons of restaurants near there. Fancier places are La Gondola, Shilohs, and Pats. Nothing comparable to New York fancy, but very delicious..
If you want to schlep, you can go to the Herzog winery in Oxnard, Tierra Sur. Food is good, but I personally don't think it's worth the schlep.