Perigueux is not large enough for an airport, but as with most cities in France, there is an SNCF station from which you can connect to and from the rest of Europe. There are daily trains from Paris, a trip which takes around 4 or 5 hours, as well as local commuter trains that run through the countryside.
Car travel is logical as well, especially if you want to tour the surrounding area at your leisure.
Most sights are reachable by foot: main attractions like the Vesunna Museum, Renaissance area, Roman arena, art museum and the Odyssey Theatre are all within a five minute walk from each other.
There is a bus system that runs through the town and to the outlying areas as well, with stops scattered pretty evenly throughout the town.
Bicycles and motor scooters can be rented from several shops, including MBK near the Office of Tourism. Prices are very reasonable, with bikes running from 10€ and scooters from 20-30€ per day.
There aren't many taxis floating around town to flag. Cabs generally must be called for in advance.
There are many caves in the area
There is a market with fresh local produce going on Wednesday and Saturday mornings