We've attacked it from a couple of directions.
First time we came from the south and stopped 1st at Lago di Santa Croce, just up from Vittorio Veneto. The camp site at the village is OK, good restaurant, lots of windsurfers and kiteboarders. There's a good track round the lake to the east.
Then we went north to Cortina. use the SP251 and then over the Passo Giau on the SP638 - amazing scenery. At Cortina we used Camping Rochetta which was OK. There's another one next door. It's a nice walk in Cortina.
Then we went north, we wanted to do the Tre Cime di Laverado walk but there was a bike race on and we couldn't get near, so then made our way north into Austria. I wouldn't recommend the site we stopped at except that the beer was good :-D.
Another time we came in from the Soca valley in Slovenia over the pass. That time we stopped at Auronzo, just south of the Tre Cime. Open site near the river with some spectacular views of the mountain at the end of the valley at sunset. Nothing special about the site but it suited us for the night.
Then we finally did the Tre Cime walk. Absolutely amazing but there's a lot of people up there! They bring bus loads up the mountain to the refuge. If you are interested in doing the walk, then there's a campsite down at the village and a white whale parking spot.
On the way out of the Dolomites, we stopped one night at Hotel Camping Ansitz Gamp at Chiussa Klausen south of Bressanone. Bit noisy with the motorway up above but a very clean site, very busy and there's a nice walk down to the village with a couple of bars. The food at the hotel was good. If I remember correctly we thought the whole thing was pretty expensive though.
We didn't stop in Austria on the way back, we'd been on the road for 6 weeks and were putting the miles in at that stage.
If you go right through the dolomites onto the plain, then go to Treviso, a lovely small town. Ryanair fly there for Venice and it's a shame more people don't spend some time in the town. And of course you can drop in on any of the prosecco farmers around Valdobbiadene to taste their latest prosecco vintage.