I'd fly into Melbourne (not the only choice) if you can afford the prices -- they're usually high and rent a car and drive down to Vero.
For day trips, you can go up to Kennedy Space Center and Cocoa Beach and Cocoa Village, Melbourne has a zoo, beaches, restaurants, a small downtown with some shops (it's not much unless they've greatly improved it since 2006). I don't know what's south of Vero until you get to West Palm and Lauderdale, so I'm not much help that direction!
There's the Treasure Museum in Vero or Sebastian (shipwreck stuff). Lots of nature - kayaking excursions on the Indian River.
I know others have posted some good restaurants, but I don't know which they were. The only ones I know are Squid Lips and Capt. Hiram's -- I'd pick Squid Lips of those two.