In reply to Russell Lovett:
The answer to your last question is easiest, if non-specific - any of the main centres is as good as the next from the point of view of choice and variety of routes, lengths and difficulty. I've stayed in Cortina (several times), Arabba, Corvara and Canazei/Campitello. All have a huge selection of brilliant routes within a short drive. Yes - answering another question - I'd say you need to have a car, unless you could get accommodation at a high (but roadside) rifugio eg the one at Sella Pass, from which you can walk to many climbs. However this would mean only a tiny bit of a vast area would be available to you.
Your suggestion of eg Inghams leads me to think you're not going to camp. This being the case a chalet hol with Inghams or similar may well suit, I think perhaps Neilson's also do them, using the chalets they use for ski holidays in the winter. Only snag I can think of here is chalet holidays are half board - you may well pay for dinners you don't get back in time to eat!
Have you looked at Colletts holidays - they too do chalets (all near Corvara) and I've a feeling you can opt for just B&B. They also have staff on hand with a wealth of experience of the area. I've not had much success finding hostel style accommodation of the typre they call in France "gite d'etape, though they may exist. I'm sure there must be many villas and apartments for rent where you could self cater.
I don't know if you've yet obtained a guide book but I reckon, though it's old now, a good start is "Classic Dolomite Climbs" by Kohler and Memmel. It's inexpensive, readily available and has a good spread of routes geographically and across the grades. In recent years many sport climbing venues have been developed which are good for days with late starts or bad weather early on. A plethora of guide books to these is available - not cheaply though. And then there are the via ferrata as well as brilliant and dramatic walking. To finish with an answer to another of your questions - the scenery is remarkable just about everywhere.
Whatever you decide I reckon you can't fail to have a wonderful time there. I haven't been everywhere (yet) but among those places I have it's my favourite. Cheers.
Post edited at 21:54