The main sights of Amiens are clustered enough to cover on foot. The cathedral, the Musée de Picardie, the Quartier Saint-Leu, and the entry point for the hortillonnages are all within comfortable walking distance. The Jules Verne Museum is about twenty minutes on foot from the cathedral, or a short taxi ride.
The city has a tram system (Amétis) and bus network for getting to points further out. Cycling along the Somme is pleasant — the city has bike lanes and rental options. For exploring the Somme battlefield memorials outside the city, a car is essentially required.