Agree with Ben on the suggestion to head to GW for overnighters. It's very easy to piece together some 15-20 mile loops in the Big Schloss area with some great views and access to Little Stoney Cr if you fish. One of my favorite loops in GW is the AT-Mau Har loop in 3 Ridges Wilderness. There's quite a bit of elevation gain, but it pays off with excellent views of the valley.
We've got a cabin a couple miles down the mountain from Big Meadows, so I spend a lot of time day hiking and fishing SNP around the Rose River and Rapidan. It's one of my favorite areas of the park, but it definitely gets crowded on nice weekends. I do the occasional overnight there, but I usually find myself hiking back out come evening. If you're dead-set on SNP, the earlier recommendation for Big Run was a solid one. The Brown Mt-Rocky Top loop outlined on midatlantichikes.com is about 18 miles, includes access to Big Run if you fish and great views of Massanutten and the valley from Brown Mt and Rocky Top. As an added bonus, I always see a ton of wildlife on these trails since the southern area of the park receives much less traffic than the central and northern districts.