Will be there in a month - looking for recommendations for good shell beaches.
Bornwithwheels may be along shortly, but I don't think there's good shelling in the area. There are areas of rock and worm rock in the area (those offshore are often popular with surfers), but even here at Vero Beach, where there's a lot of shell sand, you don't see so many good fresh specimens. The best shelling ever was just after each of the hurricanes in 2004.
Here's a look at a useful reference that will identify most of what you see, Florida's Living Beaches by Blair and Dawn Witherington.
The clear water is unlikely to last, but here's a fresh video of rock exposures in Satellite Beach:
And here, some idiotic young male behavior at the Doubletree Hotel. At least you can see that it's a nice hotel.
It's hit and miss with shelling, tides, wave action and number of people on the beach can make a difference. However if you don't find many on the beaches near Indialantic take a drive south to Melbourne beach (about 10 miles). There are some county parks there with beach access ramps and shelling can be pretty good down that way. We don't have the variety that the gulf coast has and many are broken due to hitting the rocks/ reef before getting to shore but there are still some good ones. You could make it a day trip, pack a cooler and drive all the way down to Sebastian Inlet State Park. Not so much for the shelling but a nice place to visit. Hit some of the beach access areas on the way down or back. There will be several. It takes about 25 minutes to get to the inlet.