Cortina d'Ampezzo, is in Italy
The most famous, fashionable and expensive Italian ski resort. In summer you may well find all camp sites full - meaning FULL.
Flying in you'd want to fly to the Venice Area, either Venice's main airport, Marco Polo, or Treviso, or Bolzano in Italy. Or Innsbruck Austria.
Driving in is the most obvious option. Cortina is not too far from the Autobahn to the Brenner Pass or there is an Autostrada that goes from Venice to Cadore some 40km away from Cortina. Thankfully the valley does not have a very high elevation so it is clear of treacherous road conditions for much of the year, be sure to check road conditions before driving and be aware that conditions tend to be far worse through the mountain passes, be sure you are driving on the most traveled passes as they get cleared first.
Cortina Express buses run somewhat frequently from Venice Mestre train station, Venice Marco Polo airport and from Treviso airport, daily off peak season and 5 times per day in high season. Journey time from Venice to Cortina 2 hours. In summer there is a daily bus service to Cortina from Bolzano through Dolomiti passes scenic road.
There is a train to Pieve Di Cadore some 35km from Cortina that comes direct from Venice (€7.50 each way) a 6 times a day during the peak winter season and takes approximately 2h45m, and then dolomitibus runs a bus that runs roughly 5-10min after arrival that will go to go to Cortina in approx a half hour, a ticket is €3 and can be purchased upon entering. Taxis to Cortina from here are €65. Similar public transport runs in summer.
Walking within the town is the obvious option, as it is relatively compact. There are also local public buses, the small orange ones which will take you in the very immediate vicinity. Connections with Dolomitibus at the bus station will take you to the surrounding towns and outlying areas, as well as to the ski areas, but do so rather infrequently. Please note skibuses do not run from 10am to 2pm, and stop at 5pm. The Dolomiti buses are very useful for hikers as they mostly go west and east to the mountain passes, from which cable cars or chair lifts ascend, and bus stops are often positioned at the starting points for hikes. Timetables for all these services are available in the bus station. Combination tickets are available for both buses and lifts and represent a good saving if you plan to be around for several days.
Taxis are generally available and can be called, some areas have a taxi stand like the bus station, or Passo di Falzarego. Taxis are VERY EXPENSIVE in Cortina, expect to pay €3 per kilometer and they typically charge from Cortina to where they are picking you up and then to your destination. I.e a trip from Pocol ski lifts to Cortina an 8km trip will cost €30.
Based on convenience and the cost of a taxi, you are best advised to bring a car. However for many that will not be possible so buses are the next best option.
One local bus goes up to the Auronzo hutte/rifugio/mountain inn, which sits directly beside the Tre Cime de Lavaredo, one of the finest mountain blocks in the Dolomites. From the refugio you can walk on a fairly level path anti-clockwise around the mountain, to get the very best views from the far side.
There are many and varied hiking routes, reached by buses, cable cars, gondolas or chair lifts, or on foot. Good maps are available, especially one at 1:25000, which have all the routes marked complete with their relevant numbering (which corresponds to the numbering on the actual paths themsleves. The Tourist Office has also a rather basic map which is also useful for orientation purposes. For the most part the routes are well marked in the usual red-white-red flashes common in many parts of the Alps.
You have a choice of 2 cable cars from the town, and the bus to the other areas in the Cortina Ski Region