Yep, it's exactly where you think it is. But hopefully the hint will help make the search easier. It is not meant to frustrate. You could also look at the picture hint).
The cache is located at the entrance to Fort Adams. The Fort opened July 4th, 1999 with much fanfare. It was named in honor of President John Adams who allocated funding to build the fort.
Fort Adams is now a state park, with boat piers and launches, and tours of the fort. You can visit the Fort's website for more information. There are some great views here, and you can spend some time walking around or enjoying a picnic lunch.
Cache is not snow friendly. The cache is not quite wheelchair accessible, because the last few feet are on grass. I suppose with the right chair it can be.