A popular pastime the area is famous for is camping with over 200 campgrounds in the region with many of the camps near the beach giving you many of the normal camping activities to choose from like swimming, hiking, biking or just relaxing.
One of the most interesting parts of Apulia is its coastline and beaches. The northwest part of Apulia where it shares a border with Campania near the town of Marina di Ginosa has beautiful white sandy beaches and continues with this kind of beach till it reaches the town of Taranto. From this point on however you have a rocky and cliff covered coast with beautiful sandy lagoons jetting into the land covering almost the entire coast where you will find areas of sandy beaches from 100 feet to 1000 feet long followed by more cliffs and lagoons. This continues down and around the entire peninsula till it reaches the town of Torre Santo Stefano. A very popular thing to do in there areas is to bicycle from beach to beach and many people bicycle just because of the beautiful views.
Speaking of views there are some fantastic views of the coastline and the Adriatic sea from many of the golf courses that can be found along the coast.
In the cities there is also plenty to do with over 100 museums in the Apulia region featuring artifacts from the Greek and Roman eras as well as some Moorish relics from the age of the crusades. Some of the highlights of the region as far as roman ruins go is the Roman theater in Lecce and the temple in Canosa.
Other outdoor sites to see could be Castle de Monte near the city of Bari and the underground cavern near the town of Castellana Grotto however I guess technically being caverns it could be considered indoors. Another town that has been getting more attention in recent years is Alberobello which has an area of town called Trulli where all the roofs of the houses look kind of like pointed grain silos and is a very interesting architectural design.
If you need additional information about a museum in Apulia you would like to see because, so many towns in Italy call there museums by the same name, the municipal museum for example you would need to do a search using the name of the museum and the town it is in to get good information and the location.
It would be great if I could provide information and a link for every city and every museum in each region but not many if any websites could really do that. With that in mind if you want information about place you heard of or a museum listed here you could try wikipedia which has thousands of people from all over the world providing them with information. Also please don't forget to come back to do your hotel search and booking once you have picked out the city you want to visit or just bookmark the links page.