One great thing about this neighborhood is the seemingly endless supply of places to try buying food and groceries. Since this topic is way too big for me to think about, I am just going to start with one category: fruit and vegetables.
I am increasingly pretty happy with the fruit and vegetables I get from the Met. Not so happy at Trade Fair, and I don't seem to enjoy shopping for produce at Patel Bros or Apna. I frequently go to Fruitel Farm on 78th but I am not always that pleased with the quality. The other fruit store a few doors down closer to Met seems to be approximately the same.
Further down towards where I live (80's) occasionally I see what look like some really good deals on fresh things from I believe it's called Kim's around 80th St. It's a tight squeeze, but when things look good from first glance, it seems worthwhile to get things there. Also there's a high turnover which is always good for produce. Further along 37th, the quality diminishes with the next place - don't know the name of it (could be around 81st) but it has high wooden shelves in the back with other cookies and cereal, etc. And the quality sinks miserably low as you get to the fruit place between 84th and 85th.
One time I got the crispiest grapes ever at the Korean-owned convenience store on Roosevelt and I think 85th or maybe it's 84th (it's where the triangle of streets comes together). Another time I went back and the fruit looked as droopy as ever.
In terms of the Asian places, I like Chonghap fairly well (though it has an odd smell. . .) and the produce is pretty good there. I never go to the Pacific Market any more after having bought some chicken there that smelled bad when I got home. And I don't remember the produce being too interesting or fresh looking.
Living in the 80's, I am almost as close to the Hong Kong Market in Elmhurst as I am to Chonghap, so sometimes I walk (15 minutes) there. They don't have the highest quailty fruit in the world, but the vegetables were extremely fresh.
And one time I took a trip over to Astoria after reading Astorians and chowhound to see where to get good produce, and I bought a head of lettuce that was still crispy after a few weeks - maybe a month (clearly I'm not eating enough salad if the lettuce lasted me a month). I think that place was Elliniki or it was the place nearby to that one.
And oddly enough, after swearing I would never ever buy produce again from a Trader Joes after the one i went to in Massachusetts kept selling me produce that was close to expired, I have found that the produce at the TJs in Queens is actually pretty good.
I've gone far and wide in search of good and reasonably priced groceries (the organic place in Forest Hills, the Stop and Shop on Northern, Waldbaums in the 70ths in East Elmhurst, Western Beef and Pathmark in Astoria/LIC. . .but this post seems long enough).