Little India is where you'll find the most mango savvy consumers and retailers. West side, not as much. If you're really a mango fanatic, make the pilgrimage from the West side. In lieu of that, try the 99 Ranch in Van Nuys, or perhaps the India Sweets & Spices nearest you.
Different varieties arrive year round in the US, mostly from South and Central America and Mexico. The most common Tommy Atkins variety are absolute crap: wooden, flavorless, and full of annoying fiber. My personal favorites from this hemisphere are the Haden and Ataulfo.
If you've not tried the mangoes from India, you should splurge on them at least once. They should start arriving some time in March. I have not checked to see if the varieties from Thailand are being imported into the US yet. A few years ago, irradiation facilities in Thailand were not quite ready to meet USDA requirements. They might be now, but I haven't researched it recently.
For more specific retailer info in Artesia, and seasonal varieties, see: