In reply to AndyCook:
Well a multiday route is not a problem. All you have to do is get benighted and hey presto
There are some enormous walls around these parts, but generally the etiquette is to go like the clappers, go light and top out in a day. Especially in the height of summer there will be many storms, usually after lunch time as hot moist air rolls in from the Med. So it's best to follow that principle. If you want to overnight on a long route, then I'd choose a little later in the year as the weather becomes much more stable - September is cooler and drier and you can get some fantastic days. Routes really depend on your grade and what you are comfortable with but you can do anything from grade IV 800m routes through to grade VII 7 1400m and beyond. Sarca as suggested can be great although that's more Brenta than the main mass of the dolomites and much lower altitude. But some of the great walls include:
Civetta NW face
Marmolada S Face
Sass Pordoi NW Face
Monte Agner N Face
Pala di San Martino
Tre cime di Lavaredo north faces
Sassolungo, pretty much anywhere
amongst many others.
Typically smaller routes, unless they are more alpine training routes are 300m+ which often you can complete comfortably in a long morning. So what sort of grade are you after?