Yes, you can shore dive off of Vero. If you're lucky, you'll come across some of the scattered remains of the 1715 spanish fleet -- mostly cannon and ballast. Vis is around 25 if the seas are flat -- and they must be flat. Otherwise, it drops to almost nothing.
If you have a car, drive about an hour south to Palm Beach (Riviera Beach Marina). For about $45, operators there will take you out for a 2-tank drift dive.
If you haven't drift dived before, the boats basically drop you in the Gulf stream current about 1 mile from shore. You follow the leader with a float ball, and 40 minutes later, you surface, and there's the boat waiting to pick you up. No effort! Check out Dive Solutions on the internet if you want to book. Weekends will probably require a few days notice.
Boynton Beach was mentioned by someone else. Excellent diving there. A little bit further than Palm Beach. Check out Dive Charter International. Around $55.
Both locations offer excellent diving at great prices.
ScubaDad