If you take Whole Foods and smush it together with an Asian supermarket, you will get something like H-Mart.
H-Mart is a chain of grocery stores that mostly specialize in Korean food. So you get the usual fare you expect from an Asian grocery, but presented in a more upscale manner than the usually utilitarian white walls, high shelves, white tile, and a few helpful signs.
There is a nice produce, fresh fish (still swimming in the tank) and meat section before the rest of the place is taken up by dry goods and the last aisle of homegoods. There is also a very good prepared food counter full of Korean goodness.
We go to the one in Edison, NJ, which is about 45 min from my place. The nice thing about this location is that its in a strip mall with other stuff, like Asian Fried Chicken, Korean Tofu, and Mongolian Hot Pot.
Also Paris Baguette, a very high-end Asian bakery. The workers at Asian Baguette don’t seem particularly thrilled about the French uniforms they have to wear (I have no idea why the theme, but the black berets do look ridiculous) but the pastries are tasty. Last time we went, I got the tiniest macaroons (pictured next to my phone for reference).