Shakespeare is my favorite author of all-time.
Also my favorite playwright (of course.)
I love his poetry...but he's not my favorite poet.
That honor goes to Mr. Eliot there...
Shakespeare, Milton and Homer would be 2/3/4 in some order...
In terms of shorter poets, Lord Byron, all the way, the Original Rockstar, and 10x cooler than Johnny Keats (though I like Keats too.)
I know Emily Dickinson's on this list, and I like her as well..."Because I Could Not Wait for Death" is, in my opinion, one of the best poems ever written by an American author, male or female; that being said, that damn meter of hers can get a bit tired after a while (hell, even Shakespeare shook things up a bit sometimes.)
Walt Whitman's gone up and down in my mind...some days I think he's underrated, some days overrated...the same goes for Allen Ginsberg...but both are at the very least "good" poets and worthy of being read (and that's probably the nicest thing you'll hear me say about any Beat Poet ever, not a fan at all.)
Langston Hughes, both in his Harlem Renaissance Period and his "Red" Period, is astounding, and needs to be read MORE. Period.
Dante's...well, Dante.
Obviously Poe needs a mention, and you could argue "The Raven" is--excluding Eliot's poetry, as that's more Anglo-American and I'd argue he's more the former than the latter--maybe the most distinct and well-known American poem in the world, and with good reason, it's simply PERFECT. In the same way I think Hamlet's "To be or not to be" speech is perfect, and that the opening paragraphs to "A Tale of Two Cities" and "Lady Chatterley's Lover" are perfect opening paragraphs, I'd say that "The Raven" is, for what it is, as perfect a poem as there is in the American canon. That being said, besides "The Raven" and "Annabel Lee," I tend to think of Poe more as a short story writer than a poet, though of course he was both...and many other things as well.
So, that's my TMI/tl;dr answer--
Shakespeare's my favorite playwright and favorite author OVERALL, but in terms of pure poetic prowess, I prefer Mr. Eliot, and I'd argue we STILL haven't had a poem that has topped "The Waste Land" (and yes, I include "Howl" in that...great poem, definitely my favorite work of the Beat Generation--though again, not a fan of that movement--but I'd argue TWL is still supreme, and has redefined poetry in such a way that we're still living in its colossal shadow today.)