Bourges (about 70 km)

Nice city with huge cathedral. Great for an afternoon out.
Montlucon (about 40 km)

A somewhat smaller town. In the old street behind the main shopping street there are some nice restaurants and terraces (at least in the evening).
Moulins (about 140 km

Slightly smaller town but cozy.
Clermond Ferrand (about 140 km)

Largest city in the list with a combination of large shops and modern shopping arcades and old streets with smaller boutiques. Also a very large cathedral in the center. Outside the city in the volcanic area of the Auvergne, a large mountain (Puy de Dome) can be visited with a train track.
Poitiers (about 160 km)

A good shopping city.
Tours

Also a decent shopping town. Good to combine with a visit to some beautiful Loire castles.
Limoges (120km)

Nice shopping town.
Nevers (115km)

Nice town. Possibly to be combined with a visit to Bourges
Chateauroux (45km)

Not a very big city, but it does have a very large Auchan, a nice 'Grand Frais', a Decathlon and a large thrift store (Emmaus) in the outlying areas.