In reply to Totally-Normal:
As everyone says Citta dei Sassi is a great location for what you're after. Though it is a bit of a drive from Cortina.
For somewhere a bit nearer Cinque Torri is excellent. There are a number of low grade routes in a magnificent setting. Take a look at the north face of Torre Terza/Latina North Face (down as the 'School of Rock' climbs in the Rockfax guide) for a few good routes that are rarely busy.