Howdy Michele!
Let me begin by answering your question regarding the airports. Approximately 90 minutes from Vero Beach are two full service airports; Orlando International Airport to the north and Palm Beach International Airport to the south. Melbourne International Airport is about a 30 minute drive north of Vero Beach. I would select your airport based on any other plans you might have during your vacation.
VeroBeach.com has some great information that might help you in your planning. There are several dining and shopping opportunities available in the area as well as some unique entertainment options.
Some dear friends of ours visited
Disney's Vero Beach Resort a few years ago and loved every minute of their vacation. They spent virtually every moment of their vacation on the resort property. They are not really "beach people" but they fully enjoyed spending oodles of time at the beach doing something they rarely get to do...relax. They also enjoyed a kayaking adventure and attending surf school.
You will find a signature dining restaurant, 2 casual dining options, a quick service restaurant and a lounge on property. Our friends stayed in a 1-bedroom villa and while they did enjoy the restaurants, they also enjoyed several meals in their villa.
I think you will find plenty to keep you busy and you can always make the short trip to Walt Disney World if you want to spend a day or two at the theme parks while you enjoy the charm of Disney's Vero Beach Resort.
Please let me know if you need any further information and thanks so much for your questions!!