The Meyer lemon is actually a cross between a true lemon and a mandarin orange. It's got a slightly orange cast to the zest and the pulp, tends to be juicier and less seedy than a true lemon, and the flesh is softer and less fibrous than a true lemon.
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They are all over the farmers' markets; they're also a very common home garden tree, so chances are you know someone with a Meyer lemon tree. If not, take a walk around; there are bound to be Meyer lemons overhanging the sidewalk in almost any residential area. Only pick what is clearly public fruit, that which overhangs the public right-of-way; don't trespass. Choose lemons that are heavy for their size (if you are picking them, look for a small bulge at the ground end of hanging fruit; this indicates that the juice is so heavy it is distorting the shape of the fruit). Surface scrapes are no big deal, but avoid fruit that has cuts in the skin. Lemons in season (i.e., now) shouldn't cost more than $1 a pound at the farmers' market.
Meyer lemons make excellent lemonade, they make excellent preserved lemons, they make excellent Shaker lemon pie. Incidentally, the flavor of Meyer lemons improves if you halve them and set them on a hot grill just long enough for them to get some char marks; the smokiness permeates the juice, which provides a great companion for grilled chicken.