Many people fly into West Palm Beach (PBI?). It's just a short drive up to Vero from there.
Other options to look at would be Fort Lauderdale (FLL) or Orlando (MCO). Both of those are somewhat larger than WPB, so they may offer more flight options. Both are also reasonable drives, but farther than WPB.
Others use Melbourne, but I think that has to be a pretty small airport with pretty limited flight and carrier selection.