In reply to leroybrown: An unvote for Long Tall Sally. It's an alright route, but Burbage North is a tiny, minor little edge which is much better for bouldering and soloing. Not exactly a high concentration of classic routes at HVS/E1 (one of each in fact, and the HVS isn't really).
Stanage and the Roaches are the obvious places for someone who hasn't done anything in the Peak, they're far and away the biggest, best crags, with loads of magnificent routes. Particularly Stanage Popular, loads of great E1s from paths like Easter Rib to sandbags like Tippler. Pretty much every style. Great HVSs too - don't miss Good Friday and Eliminator, which could be overlooked but are among the best.
A great day would be Hen Cloud, not so much for ticking E1s (I'd go to Stanage Popular for that), but for big, butch HVSs that will live long in the memory (they're
much harder than Stanage E1s). Perhaps a bad choice for intro to the Peak though, unless you're good at jamming. I wouldn't bother with Cratcliff unless you want brilliant E2s, or just one great HVS. There's nowt at E1.
Curbar is good if you want a really hard time - The Toy, L'Horla, Soyuz.
Froggatt if you want to get scared on slabs (if you like them, it's easy to push up to E2 there), and do a few hard HVS cracks for variety. Rather busy on a weekend though, with not as much to go round as Stanage and the Roaches.
On the limestone, I wouldn't go near Stoney (dump, polished, choss-heap), High Tor is spectacular, and I would have thought Chee Tor will be super-minging.