Avignon is perhaps most famous for its bridge, the Pont d'Avignon but there's a lot more than that to see in the large walled city than that.
The city was used as the base for the Pope from 1309 to 1377 and courtesy of that there's effectively a mini version of the Vatican right in the centre of the city. This consists of the Gothic style Palais des Papes (very much a fortified palace with 17 foot thick walls) that was built between 1335 and 1364 and the Romanesque style Notre Dames des Doms, the cathedral just beside it. Naturally, there are lots of churches around the city dating from around that time period.
In the same square you'll find the Musée Carnavalet which has quite an impressive collection of Renaissance paintings.
Usually walled cities are quite walkable but Avignon is enormous so you need to be selective rather than trying to see it all in one go. That's not such a loss as you might think as much of the town inside the walls is of quite modern construction. The little train offers a good chance to see most of the highlights of the city over the course of around 40 minutes.
The Pont d'Avignon (really Pont St-Bénézet) is famous due to the French song but isn't particularly special.
Avignon airport (AVG) is served by FlyBE; you've a wider range of flights at Nimes (FNI).
You can get there by Eurostar from London during the Summer but otherwise you'd need to change trains in Paris or Lille for the direct TGV service.
