(Maybe Martha, with her background in Spanish, could answer this.)
In the United States, from what I've heard, the common pronunciation is Bar-bAY-dos and Gre-nAY-da.
But if these are derived from Spanish, I would expect to hear Bar-bAH-dos and Gre-nAH-da instead.
How did this come about?
(Similarly for Colorado - short a, or AH?)
I've always heard /bar 'be dos/ (approximately "bar-BAY-dosse") for the one. For "Grenada" I hear both /gr@ 'na d@/ and /gr@ 'ne d@/ ("greh-NAH-dah" and "greh-NAY-duh").
I've observed that roughly speaking, repeat roughly, Brits convert a foreign word's pronunciation to whatever the word looks like to them, while Americans make a stab at the native pronunciation: Thus Brits say "men-AG-you-a, nicker-AG-you-a" and the Yanks stick to "men-AHG-wa, nicker-AHG-wa". But any US place name that starts as a foreign word is pretty soon coöpted into the local dialect; in North Carolina there's a Benaja Road (pronounced /bEn 'e dZ@/ (ben-AY-dja), and Medina county in Ohio is pronounced meh-DINE-ah. In Arizona and southern California maybe the tendency to Americanize Spanish words is reduced somewhat, but I wouldn't place any bets on it.
Bob's observation about the Brits might also explain their classic Jaguar automobile, which I grew up pronouncing as (two syllables) "JAG' GWAR." But of late, a new 3-syllable pronunciation as "JAG' YOU ARE" seems to be catching on. I've even heard it pronounced that way by sportscasters referring to the NFL team from Jacksonville.
Yes, I heard the British pronunciation "JAG-you-are" some decades ago, I think in reference to the sports car.
By the way, one exception might be French words. France, after all, is a neighbor, and more Brits than Americans speak French, so it may be that they get the French pronunciations more often right than we do.