This is very, very good. It needs only a few small, but important, changes to make it excellent.

British Virgin islands

The British Virgin Islands [we would use "the" to start this title and we capitalize all important words in a title.]

Yesterday I read some articles published on the online edition of travel magazines that I usually consult.

Yesterday, I read some articles published in the online editions of the travel magazines I look at regularly. [We use "in" for a publication, even one online. Editions needs to be plural because you looked at more than one. "Consult" is used more if you were researching rather than reading or "looking at." You could say, "that I usually look at" but "regularly" sounds more natural here.]

While I was reading I dreamt about how spending holidays in those islands could have been amazing.

While I was reading, I dreamed about how spending holidays in those islands would be amazing. [This is a minor point, but "dreamt" is used for dreams when you are sleeping, "dreamed" when you are awake and thinking about something. "Could have been" implies that you had a chance to do it but passed it up. "Would" means you'd like to do it in the future.]

Apple Bay, Cane Garden Bay, Virgin Gorda and Anegada with their white sand and turquoise waters invited me to reach the beaches, relax at the shadow of the benjoo trees and enjoy the Caribbean "way of life" eating a callaloo or a conch.

Apple Bay, Cane Garden Bay, Virgin Gorda, and Anegada, with their white sands and turquoise waters, invited me to lie on the beaches, relax in the shadow of the benjoo trees, and enjoy the Caribbean "way of life" eating a callaloo or a conch. [This almost perfect. "Reach" isn't right, unless you mean "reach out and touch". "Lie on the beach" is what you do. You are "in" a shadow.  I added a few commas to set off the descriptive clause about the waters and sands.]

Thanks alot :)

Thanks a lot. [ "A lot" is two words.]

Bravissima!

As I was reading travel magazines, I imagined holidays on Apple Bay, Cane Garden Bay, Virgin Gorda or Anegada, with white sands and turquoise waters. I want to go to a beach and relax under Benjoo trees and enjoy the Caribbean way of life; eating Callaloo or conch. 

<em>What is a Benjoo Tree? Anyway - if you decide to go, buy an extra ticket for me!</em>