From Buxton you can pretty much get anywhere in the peaks in an hour or so. Some of my favourite places are Ashford in the water, really nice village with river walk to Bakewell (we always park in Ashford and walk to Bakewell as it's free..... I am a tight Yorkshireman after all). There's some great spots in Ashford village for landscapes and lots of old chocolate box cottages to shoot. Bakewell itself also has great locations like cobbled streets and along the river but can get quite busy. I tend to visit as early as possible.
Lady bower is a must, as is Castletown, mam tor if your up for a brief hike, winnats pass offers great photo opportunities, there's a few blue john caves in the area too along with a castle ruins on the hillside. Depending on the wind, parasailing is very popular in Castleton on the hill to the side of winnats pass, so photo opportunities there also.
Not sure about waterfalls in the peaks but with all the rivers there's bound to be plenty, try searching good old Flickr.
There's a village called foolong (or similar) where a friend of mine lives, at the minute there's barn owls which he spends lots of time photographing.
Chatsworth house is worth a visit this time of year, and I can highly recommend all the other locations mentioned previously by other forum members.
Have fun, look forward to seeing your shots.