Hi there, am new to this site but thought I'd offer my advice on Burleigh.
I've lived on the Gold Coast for about 5 years now (originally moved to southside of Brisbane in 2002) and am loving it!
All up the whole coast is pretty hard to beat for a great way of life but Burleigh is definately one of my favourite areas (I've been working at Burleigh Heads for 2 years). Burleigh Heads itself has still got a bit of it's own character and (as yet) hasn't been overrun with ugly high-rises and has it's own defined high street with cafes, small shops and banks etc.
Family homes aren't cheap in/around Burleigh Heads and most of the larger homes tend to be situated a few streets back from the beach but still only a couple of minutes from the beach.
Burleigh Waters is situated further west from Burleigh Heads and is a bit more suburban but it is a well situated suburb with easy access on to the main roads of Reedy Creek Road (which runs east/west from the main Pacific Motorway to/from Burleigh Heads) and Bermuda Street (which runs north to Robina/Southport etc). The houses in this area vary from the water-front "Mac-Mansions" to small 3/4 bed average family homes... depending on the street block sizes can vary quite a bit.
If you wanted to head west of the Pacific Motorway (but still keep in the Burleigh vicinity) you've got Reedy Creek (a mix of older and newer properties) or slightly south-west is Tallebudgera and West Burleigh (a bit older but you'd get larger blocks and more of a country feel).
Anyway the whole Burleigh area is really central for the Gold Coast - you're only 15 mins to Coolangatta airport; 15 mins in to the commercial area of Southport/Bundall; maybe 25 mins to the theme park corridor around Coomera; and on a good day maybe 1-hr to Brisbane (although don't think about commuting it for work... the Gold Coast to Brisbane run is a shocker at peak times!!).
As for public transport there are pretty regular buses along the main routes and there is an extension being worked on at the moment for the rail line - from what I've seen it ends around West Burleigh and runs north to Robina/Helensvale/Brisbane etc.
Feel free to drop me a line if you've got any more questions - definately have a look at
Real Estate, Property, Land and Homes for Sale, lease and rent - realestate.com.au for properties.
Good luck!!