Congratulations on your wedding.
Do a search in Trip Reports for the Burj al Arab...Uli did a fantastic review there and I don't think the rates are that high!
I'm surprised you say that airfare to Thailand is so high. At the end of April you should be able to get there from pretty much anywhere in the US for well under $1,000 pp. This would leave you with about $4,000 for room and food. While it may not be the swishest place, you can get pretty good beach accommodation for under $100 per night. For two weeks that would leave you with $2,600 - more than you can possibly spend on meals and activities!
Now Thailand is not the most exotic place anymore, but for beach value, Phuket, Ko Samui etc are tough to beact on price.
I would avoid much of the south Pacific since food/drink is often quite expensive.
Have you looked into some resorts in Malaysia (Pankor etc?). You might even want to be adventurous and try Vietnam.
South Africa is a long flight from the US, but once you're there, prices are very reasonable. No great (swimming) beaches (unless you head to Durban and further north) since the water is so bloody cold, but beautiful scenery. Safaris are expensive.
What about the coast of Brazil north-east of Sao Paolo/Rio...there are some beautiful resorts there at fairly reasonable prices, and flights should not be a problem.