In reply to Andrew Musgrove:
Shepherds crag is a good place to start. Close to the road, dozens of quality routes and a good spread of grades. Little Chamonix at VDiff is a classic. Aardus at MVS. Adam, Eve, Fisher's Folly all great at VS and Kransic Crack Direct is a good HVS. To top it off, there's a cafe at the bottom.
Once you've done those head down the valley to black Crag for Troutdale Pinnacle, a super classic Severe.
To finish off, head to The Napes from Seathwaite and do Tohpet Wall and The Needle both at HS, and climb Innominate Crack (VS) on the way back.
Of course, there are other options that involve leaving Borrowdale. Eliminate A on Dow is possibly one of the best VSs in the county (and therefore the country), though Dow may be a bit damp and chilly a the minute. Castle Rock in Thirlmere is also a good bet for long single pitch routes on the south crag (avoid the north crag, there's a huge block waiting to fall off) and is low-lying and south facing for a bit of sun. Gazebo is a particularly good HVS.