When you say your budget is "Not more than a couple of thousand dollars" do you actually mean $2,000 or is it really something less??? in order for anyone to be of help we really need to know what your budget actually is (try to be as specific as possible). Tell us too, how long a honeymoon you are planning. Also, is that budget just for accommodations or does it include your meals and/or activities while on your honeymoon? Lastly, does that budget include your transportation costs to the final destination? If so, you have to let us know where you are traveling from and your preferred mode of transportation - car, train or plane.

Now, many of the Florida Keys don't have beaches or if they do the beaches are tiny. You may not be able to find "pretty private" beachfront or even beach access accommodations for a budget of "a couple of thousand dollars" as privacy and beach front often come at a steep price. You might consider renting a place that is a few blocks from the nearest beach as that will save you money.

There are a number of condo type units throughout the Florida Keys that you can rent for around $1,500 to $2,500 per week in May. You can find plenty of listing by going to the TripAdvisor website. Click your way through to the Florida Forum then use the dropdown menu to select "Jump to a more specific forum" and choose "Florida Keys". On the left side of the Florida Keys page you'll find a link for "rentals" - click it on and you'll find links to scores of properties, many of which are in the price range I mentioned.

Another suggestion would be to look at rentals on Senibel, Captiva or on Amelia Island, you may find some nice places in your price range. Also check out rentals in the Destin area. These areas all have some beautiful beaches that are among the best in Florida.

Good luck in your search.

http://www.theinnatturtlebeach.com/

or

http://turtlebeachresort.com/

vrbo.com is the shopping place for owner rented condos and cabins. May could be late enough for prices to drop in your budget range.

There are affordable beach cottage rentals at Indian Rocks Beach and I have seen others at Cocoa Beach.

If you want a beach destination, you'll be disappointed in the keys. The keys are coral, and nearly all the beaches are man-made and tiny.

Sanibel/Captiva is what you are looking for...

The editors have given you the best suggestion of all -- for a really inexpensive Florida honeymoon go to Rio! Huh?

Actually Sanibel is a great idea for a "quiet" honeymoon and a somewhat secluded beach front place. And while Sanibel is generally not cheap, you can definitely find FANTASTIC prices on VRBO or elsewhere during May if you want your own apartment rather than a hotel or resort.

Check out Destin.

We really like the Keys. The drive from Miami to Key West is beautiful, especially from Key Largo down. As others have said, Key West does not offer much in the way of beaches except small manmade ones at the expensive hotels. I would recommend for your consideration this Hampton Inn in Islamorada: http://keys-resort.com/ It would be on the beach and you could easily drive to Key West as a day trip. You could also visit Bahia Honda State Park which is beautiful and snorkel at John Pennekamp State Park http://keys-resort.com/ I have not personally stayed at this Hampton but it has been recommended on this site before and you could check out the reviews on TripAdvisor

We also love the Keys, but they are very different than what the OP asked for... We also have stayed at the Hampton on Islamorada and its not a house or cabin on the beach... its a Hampton with an Outback and a trucked in sand beach on a breakwall... far from a "dream honeymoon"

Thanks garyt22 since you stayed there you would know if it is romantic or not. Sorry Joel