We camped too; the campsites in Cortina are pretty good. There are three close together just south of the town. "Dolomiti" was a bit nicer than "Cortina"; we didn't look at "Rochetta".
Cortina area? Hmm. From my limited experience (two trips): if you're a small, focused team and you get lucky with the weather, there's better climbing elsewhere. Pala, Sella, Marmolada ...
Cortina otoh has the big advantage of having a lot of very accessible shorter stuff around the Cinque Torri / Falzareggo Pass for iffy weather & easier days. It certainly has the something for everybody factor: I think on one day in my group my mate & I did the Third Tofana Pillar as our first proper Long Route, the big boys did the Comici on the Cima Grande and the others went cragging on the Falzareggo Pass. Everybody happy.