My first thought was Wentworth by the Sea in the Portsmouth, NH area, a Marriott property. Not exactly "countryside", but there just isn't much in the luxury department outside of the major metro areas in New England.

Not sure if your points options would allow for Omni hotels, but the Omni Mount Washington in New Hampshire is magnificent.

The Doubletree Bedford Glen in Bedford, MA is not TOO far in the countryside, but it's at least a very nice property in a very wooded area.