We enjoy hitting the antique shops while down at Vero, also.
If you turn right out of the resort and take the causeway that Mike mentioned, you'll shortly come to US1.
We have returned to a shop just a short distance from there on several trips. I'm sorry I can't be positively certain, but I "believe" that you turn south towards Vero proper. It's on the right-hand side of the road (west side?) - in a stand-alone "barn-type" of building. It has numerous "booth" type areas containing different people's consigned items.
We always find some really interesting items in there.
We've driven into Sebastian, but haven't found too much in there.
They give you a book in your room that lists local points of interest - including shopping destinations. I'm pretty sure that many antique shops were listed in there.
Oh yeah - there's also a pretty neat one down across from Mr. Manatee's restaurant. A little pricey - but some neat stuff.
Have a great trip!