A visit to the Roman amphitheatre is a must in Nîmes, apart from the fact that you can see if from various points throughout the city, it's a truly wonderful piece of Roman heritage that is still in use today. The Musée Archéologique houses pre-Roman, Roman and Gallic artefacts and displays.
If you have transport (or have hired a bike) then a trip to the iconic Pont du Gard will be worth the effort, situated 20km N/E of the town, and this aqueduct dates from c.19 BC. Again a magnificent example of Roman architecture and an imposing structure on this beautiful stretch of river.
Also outside of the city is the wonderful Gorges du Gardon. A beautiful place for hiking, cycling and relaxing with a picnic. To get a better idea of what to do there have a read of our sight review, 'A day out in Nîmes'.