We just returned from St. John and stayed at a property that matched your requirements almost exactly. Check out
http://www.vrbo.com/398012 Called Harborview, it is located just above the Lumberyard complex and just around the corner from the Dolphin market. We walked into town in about 5 minutes, easy walk downhill but a little more effort back, although we found it quite manageable and we are just south of 60. We stayed in the 2 bedroom upstairs and the property is not luxurious but is very comfortable and super convenient. You have a pool to relax in and fantastic views over the harbor and over to St. Thomas to watch the lights. Great sunset views as well. Beaches will be either a half hour hike to Salomon and Honeymoon or a cab ride to any of the others. Snorkeling between Salomon and Honeymoon can be good, we found Maho had tons of turtles, rays, and even a couple of 2 foot reef sharks.