Using my 2009 guide data, the Partnership Shelter is at mile 526.7 (from Springer), and Pearisburg is at mile 625.9, so you're talking about a hundred miles or so of trail.
Partnership Shelter is one that most thru-hikers remember, because if possible everyone arranges to call for a pizza to be delivered there --- my hiking partner and I did about a 25-mile day to get there to do exactly that.

In terms of most interesting parts, I recall a little ridgewalking (I recall it because there was a thunderstorm at the time) somewhere north of Walker Gap and before Jenkins shelter. I know there is a "bald" or two (or more) in that general area too, so better than average chance for views in there.

Angels Rest just before dropping down to Pearisburg is worth stopping at to take photos and look down from for a while.

Really, I don't recall much in particular in that area, but do have overall happy memories of walking through it. Given your situation, I would suggest just meeting whereever schedule or trail access or other logistics works out best for you rather than trying to pick a particular "best" part in there.

Note also that I've only been through there once, and there might well be great things that I missed or have forgotten, so I defer in advance to anyone local or otherwise with more intimate knowledge than I (!).

Was just there s couple of weeks ago. The angels rest is as beautiful as ever, though I was there too early for the flowers. The trail down has been improved a great deal since I thru-hiked six years ago. It now has switchbacks and a really good treadway (Konorock maybe?). Incidentally, you don't have to order pizza at Partnership, the joint is in walking distance and you can resupply while you're down the hill. And the hot shower is to die for. best, jcp