Hi!
I love Vero - you can do a search and find a lot of info on it but I'll try to answer your questions:
THe beach is incredibly close (so close the resort will probably be in the ocean before 2042). But it's east coast - not gulf - so it is narrower than St. Pete. It is clearer than the ocean water at say Hilton Head - but it is fairly rough, as it is the ocean, and not terribly clear. People sometimes surf on it and the surf gets strong, so little ones should be watched carefully. What I like much more about the beach than st. pete - is that there isn't massive amounts of shops and stuff built up on it. There are condos, and the resort - but it's more private feeling.
There is a mall about 15 minutes away. Most everything is about a 15 minute drive in one direction or the other. But since the pool, beach, and restaurants are on site, you don't have to leave. And across the road, the resort has tennis courts, Volleyball, basketball and soccer fields. THe town of Vero is really cute I think. There are a lot of good restaurants - many closed after the hurricanes a couple years ago - but there are new ones now. Gloria Estefan just opened a new hotel in town, with a cuban restaurant. There is a museum in town, a botanical garden, treasure museum, and a nature preserve. You can go kayaking on the Indian River, and there are airboat rides if you want to see alligators. I know some people say they get bored after a couple of days there, but I never do. We've stayed 5 days, and I am always sad to leave!