The swim spot at Seneca is in the parking area for climbing. Coming in for climbing go as far left as you can and park your vehicle (1/4-1/2 mile). Follow the trail at the end of the parking lot to the North Branch of the Potomac. Also, Yokums did provide horse back rides to the North Fin of Seneca. Mrs Yokum once told me that they owned Seneca Rocks until the state came and took the property from them for a bargain price but they still owned land right up to the North fin.
As tradmanclimbz said Green Wall, Pleasant Overhangs, West Pole and Ecstasy are all great 5.7 routes. Banana 5.6 to Gunsight 5.3 provides some easy climbing with exciting exposure to the top. Conn's West at 5.4 is another classic not to be missed. Prune at 5.7 is not for the 5.7 leader as there is a tendency to not place protection where you should on the crux and a slip results in damaged ankles (usually broken). Skyline Traverse at 5.3 can be exciting esp when you have to step over the void across the Drop Zone.
Crack of Dawn, La Bella Vista and Cottonmouth are excellent 5.10 climbs. Triple S 5.8 eats up a lot of nuts and can be rapped after doing pitch 1 which is the money pitch. If you are looking to climb harder there are some excellent 5.11s and 5.12s to be done. The Southern Pillar section requires you to use private property so be respectful, sometimes it is closed to the public.