You could also have a look at Angle Tarn, Sprinkling Tarn and Styhead Tarn, three of my faves.
Anywhere up on the Langdale Pikes, you can find somewhere out of the wind and near a water source, if you need it. At the end of Red Tarn is quite nice, near Pike o' Blisco
As said above, Seathwaite Tarn, behind Coniston is good and enough space for a group of you. You may also consider Blea Water (just east of High Street), or Grizedale Tarn down from Helvellyn.
I've high camped at all of these locations many times without any issues. Nobody is coming up at 8pm to collect camp fees!
The only evidence of your stay should be some flattened grass and all will be well. Have a great trip.