David wrote: "southern JMT -South Lake to Whitney Portal
100ish miles, the best alpine scenery in the lower 48, high lake fishing, great weather. Ideal time is more late July to early August when the snow and bugs are mostly gone."
I feel a devilish urge to be contrary :-)
If they've never seen Yosemite Valley, it's definitely worth seeing. This is an argument in favor of the northern half of the JMT rather than the southern half.
IMO the southern half isn't more scenic than the northern half. It's just different. It's higher, and the geology is different.
There is no opportunity to resupply on the southern half. On the northern half, you can have a very low pack weight, because there are so many places to resupply.
In a typical snow year, early July would be fine. The disadvantage of doing it later is that that's when everyone does it, so you don't get solitude.
The OP specified a one-week hike. Most people take closer to 3 weeks for the JMT rather than 2, so doing half the JMT may not fit within their one-week time frame.
As a counterproposal, assuming they haven't seen YV, I would suggest the northern portion of the JMT from YV to Vermillion Valley Ranch, in early July. (If they've already seen YV, another possibility is Tuolumne to Muir Trail Ranch; a wilderness permit might be easier to obtain for this section.)