TPC at Sawgrass is about 3-3.5 hours north of VB resort, just south of Jacksonville and not too far from the Georgia border. A bit of a haul.
As for his concerns of no golf around Vero Beach, he is sadly (or rather gladly)mistaken! Although there are no Top-100 courses nearby (like Sawgrass or Doral), there are several quality courses within 1/2-hour of the resort, and they are a great value. IMHO, I think the golf around VB is superior to that in and around WDW, particular when cost is factored in.
Sandridge (2 courses) has already been mentioned, and I think they are as good of Florida-style course as you will find. Sandridge was designed by Ron Garl, a very well respected and prolific architect, particularly in Florida. Others around the area that I have played include The Habitat, Fairwinds, and Sebastian. I would rate these in that order. Despite all being municipal courses, they are quality layouts with generally good conditions. They can be busy in fall-winter-spring, particularly on weekends and weekday afternoons, but they are all reasonably priced around $50 or less.
Other courses around or just over 1/2 hour include The Links at Pointe West and The Majors (an Arnold Palmer course). While I haven't played them yet, I hear good things about them (particularly the Majors).
If willing to drive an hour, several more quality courses become available, including 3 top notch courses at The PGA Village in St. Lucie designed by Tom Fazio and Pete Dye, and Hammock Creek designed by Jack Nicklaus. Haven't played these yet (are on my list for next visit), but they are highly regarded and designed by big name architects. Other reportedly good public courses are also within 1-hour.
I also believe Disney can get you on Indian River Club, a top-notch private course in Vero Beach, but it's pricey over $100.
Here is a link to a website that discusses and reviews all the public course along the "Treasure Coast" (essentially includes everything 1-2 hrs north and south of VB.
http://members.aol.com/saupere/treasurecoastgolf.htm