Why are vacation packages so expensive from the US? Am I looking in the wrong places?

Hi! I'm trying to find a beach vacation of apx 7 days in mid July and it seems to me like vacation packages are so expensive in the US. In Europe, I would always get a so-called "cancelled charter trip reservations" (afbudsrejser in Danish) (don't know if they're really reservation cancellations or if that's just promotional language). For example last summer my partner and I went to Crete from Copenhagen for only $450 per person after all taxes and fees. It 7 days in small cute motel including airfare (it was a chartered flight) and we booked it about 5 days in advance through http://www.afbudsrejser24.dk/. Looking there today, I see the deals are still of the same magnitude.

How can I find such deals for beach destinations (e.g. Caribbean; anywhere decent would do) from the US east coast? I'm not looking for fancy hotels or all-included resorts: I like to explore and make my own vacation without anyone planning it for me. I just need a place to rest my head that's clean, and airfare. I looked everywhere, I think, but it seems that despite advertised prices like "$400pp for 5 nights" in the end, after adding 2 nights and changing flight origin to NYC and after fees and taxes, it always comes out to no less than $1k per person. I'm really hoping that I just don't know where to look and it's really possible to get better deals (esp. if I don't care for fancy hotels).

Please help! I need a beach soon. Thanks!