This park has fantastic trails with varying degrees of difficulty and good accommodations for backpacking. Stony Ledge is the best view in the park - don't miss that. The Deer Hill backpacking area was more primitive than the Sperry Road walk-in campground but both were still quite secluded. The lodge at the summit of Greylock is worth checking out. Next time we'll spend more time in The Hopper - other hikers we talked to said that's the best part of the park
I went with a group of 4 in mid-July. The campground was clean and well-maintained but the sites are quite small and close together. There were a ton of kids and it was pretty noisy until about 11pm and then starting again around 7am.
The hiking in the area isn't great. There are a few trails but not a lot of interesting features and very little elevation change. The biggest pro is that it's only an hour from Boston.
Checking in is a big process here - it took about 5-10 minutes to get past the front gate because they ask for so much info about your party.
One additional perk is the rangers leave you completely alone.