My sisters and I are trying to take a trip for my parents anniversary. We had originally planned on Tahiti, Bora Bora, or Atlantis The Palm (in Dubai). The only problem is those places are very expensive. We can pull together for those, but is there any other place that is similar to them (beach, cool, nice) but not as expensive?

if you want a beach that is nice and cool i suggest the Mauritius. It is a beautiful place, you will surely enjoy. They have a lot of water sports and the hotels has romantic arrangement for the couples that your parents will surely love.
how about Guilin?guilin is a charming city in China.It has a warm climate,crystal Li River,green mountain and many landscapes,such as elephant hill,and seven stars park.
you can go for a travel in summer,you won’t be disapoint.
wish you have a nice trip.
Since Dubai is an option you already have I would suggest research more about it, Dubai is a wonderful place to visit and spend time in with all kinds of activities. You can make it a very economical and wonderful trip to Dubai if you plan it wisely. A stay at the Atlantis is not neccessary, one can just visit the place and stay at another wonderful hotel at much more reasonable prices. Look around for deals and you’d be surprised what great options and prices Dubai has these days.
The source that i have refrenced offers a free service that can maybe guide you if you email them with specific questions, and its a wonderful guide to the city and its attractions.
Hope this helps with your decission.
I would recommend an island circuit in French Polynesia that would include at least, Tahiti, Moorea and Bora Bora!
You can find pretty good deals these days…