The great range of the High Peaks is one of the most rewarding things to hike in the park.  The range itself is 7, mostly close peaks with a side peak of Sawteeth that also hits the 4000 mark.  This is not one of the easier hikes to do.  I know from experience as I've done 4 of the peaks back in College, and we had an Alaskan with us that was used to backpacking and hiking in Alaska, and she had trouble with our trails.