As a former Amiénois, I am biased, but there's some great, hearty food to be had in the city - and the cathedral and Quartier St Leu (as well as the Marché sur l'Eau and the Hortillonages) are pretty special. Make sure you try some
ficelles picardes and some local macaroons (far tastier than the overhyped Parisian rubbish
)
Old favourites include Les Marissons and Au Relais des Ofevres, for a more down-to-earth brasserie, Le T'chiot Zinc, on the rue des Trois Cailloux. Having said that, things may have moved on these days. But this is hunting and gathering country, and you're right next to Normandy - look for game, all sorts of wild mushrooms, and lashings of cream...
If you're driving from Amiens up to Lille, you'll probably end up heading up the D929, which takes you through old WW1 country. It's at least worth going through central Albert to look at the golden angel, but the monument at Thiepval and trenches/cemeteries at Beaumont-Hamel are the main sites. I appreciate that this may not bee the correct mood for any given trip, but it's a fascinating and sobering bit of history.
Beauvais is pleasant, and has rather less to it than Amiens, but the cathedral, once again, is rather stunning. Its height needs to be seen to be fully appreciated, and the astronomical clock is great as well.
Further north, there's Arras, worth a look in for a Croque Monsieur on the Grand'Place at least. A very Flemish-looking town, this one.