Beaches from Hamilton?

So much of the information I'm finding is Dockyards based, but we'll be in Hamilton with the Veendam. We're planning to visit the rest of the island, of course, but it would be nicer to know some beaches to go nearby and how to get to them.

I'm looking for pretty beaches that are good for swimming and have some shade available. I don't really care about snorkelling; I'm just looking for some easy places to literally immerse myself in Bermuda's beauty.

Elbow Beach, which is a beautiful public beach is about a 15 minute ride on the #7 bus from Hamilton. Don't expect to find shade, however. You can also go to Warwick Long Bay and Horseshoe Bay on the #7. You're no further from those beaches than those coming from Dockyard.