Philippine Market ?
There's a few in carson:
Take the 110S towards San Pedro, exit carson, turn left, about a mile later there's a minimall with a Seafood City (LOTS of philipine goods, like a Philipino VONS or something...fish, groceries, coconut milk, etc) plus a Jollibee, Red Ribbon, Pan del Sal shop, and Chow king (good halo-halo) in the same mini-mall as well as a import goods place. Cross Street is main. I like going here rather than vermont area b/c there is less traffic, its closer to me, and i hate going near that area.
If you turn right at Main Street, there's another philipine grocery store on the left side of the street....i dunno where exactly, but less than a mile on the left side of the street....there's a jack-in-the box and a mami-king in the same strip mall area.
Also, there's a bunch in cerritos (far) not hard to miss...forgot what street they are on...but the ones in carson are pretty good...
Go to the new Bahay Natin Phillipino restaurant in the mini mall a block East of Versailles (used to be Cafe Mambo) on the South side of the street. They serve steam table combo plates. A 2 item combo is 4 bucks. I bet they would know the location of the nearest Phillipino market. Try a sample of the bitter melon dish. Tell me that isn't an acquired taste. Food is very good. Steam table versions of various stews so the dishes are not srtingy, dried out messes. Items are tender and juicy. Who knew Tofu could taste so good.
Between the 60 & 10 freeways in West Covina, at the intersection of Azusa and Amar, is a concentrated cluster of Filipino businesses. You will probably have a choice of 2 or 3 markets, as well as specialty stores like bakeries and butchers.
Someone may chime in with something from the Westside, but this is a fallback, just in case. Hope it helps.