What cities would you recommend to visit in northern france?

It depends why do you mean by northern... the northern half of France ? There is Paris, Versailles, Fontainebleau, Rouen, the Mont St Michel, Bayeux, Etretat, the Chenonceau castle, Chambord, Chantilly, Pierrefonds, Reims, Burgundy, Franche-Comté aera (with many lakes, mountains, Besancon city), Vendée region (nice beaches and islands), Island of Ré, Oleron, Yeu, Nancy in Lorraine... That is what I can think of now in the North of France!

There are so many of them and they all have so much history and architecture to look into..some more fashionable than other of course but all with their regional foods and wines ..I would not know where to begin to plan a tour of the region. In your place I would find a hotel anywhere in the region, reasonable priced and comfortable, and drive to a different town or city every day, then back to the hotel in the evening until I had run out of reasonable close places to visit, then I would move on to another hotel and do the same again. If you can afford to stay in or near paris then so much the better, the network of roads northwards is pretty comprehensive..or, of course, you can always travel by train. If you are on a tight budget then why not get adventurous and buy a rail pass for the duration of your visit and try to arrange things so that you travel at night and for fairly long periods at a time..sleep on the train and then have a day sight-seeing and bck to a train unless you decide to stay in a hostel every few days for the benefit of a real bed and proper bathroom facilities.

Im a history fan-- loved the region of Normandy and all the wwii sites and museum. go to the dday beaches. go to Bayeux and Cain and the many little towns around there. there's a great museum in Cain

Rouen, to visit Joan of Arc.