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.
The plan is as follows. Thursday night, hike in to somewhere around Johns Brook Lodge and set up camp for the night. The trail is well used and not really that bad, if memory serves me. The total mileage is 3.6 miles.
Friday, I will do the bulk of the great range. I'll head up to Lower Wolfjaw (4175', #30) then head over to Upper Wolfjaw (4185', #29), Armstrong (4400', #23), and Gothics (4736, #10). At this point, if I'm still feeling good, I'll do the spur over Pyramid (not a high peak) and get Sawteeth (4100', #35) then back up Gothics and go back the way I came, back over Armstrong and Upper Wolfjaw and back to camp. This is for safety reasons. The trail up the west side of Gothics (Saddle Back side) requires the use of cables to go up a steep scramble. I just watched a video of a couple people going up that, I do not want to do that, nor do I think I would feel safe doing that up, much less down. (see https://www.youtube.com/watch?v=Pj5ZJUSUsiU). This makes it a 11.1 mile day with 5100' of elevation gain/loss. I can knock 3 miles and a couple thousand feet off of that if I don't do Sawteeth. It all depends on how I feel on top of Gothics, and when I get there... if I'm there by 11, I may very well do it.
Saturday will be easier in that it's only 3 peaks. I'll head over to Slant Rock and go up Haystack (4960' #3), and come back over Basin (4827', #9) and Saddleback (4515', #17) and then down to camp. This is slightly shorter hike at 10.3 miles, and 3830' in elevation gain.
Sunday, will be the day to catch the one peak off of the Phelps trail that I haven't done... Big Slide (4240', #27). This is a quick up and back and then grab my pack and hike out for 7.6 miles, 2000' elevation gain.
It will be a long weekend, and I expect to get at least 8 of the 9 peaks. If I don't get sawteeth, I'm not worried, I can get that from the AMR side of the range at some point later. I already left 2 peaks hanging, a third from the same parking lot is not a big deal.
If I get all of these done, I'll have 26 peaks this year, 29 all time, 4 done a second time. At this moment, having seen the face of Gothics and what it looks like to go from it at 4736' to Sawteeth at 4100', I probably will not do Sawteeth, so it will likely be 25 peaks this year, 28 all time, 4 done a second time.