Just to chime in, we stayed at the Doubletree for a week without a rental car and made the walk each morning and evening. The morning walk was awesome...easy, sunshine, full of energy (pushing one umbrella stroller.) The evening walk? Eh, not my favorite after a long day...but still do-able! It was about 20 minutes door to gate, but it honestly doesn't feel too terribly long. Don't feel bound to the shuttle...you could do this for a day or two!
Note that this is written by a woman who hates physical exertion.