Our hotel is in Bologna for 7 day's. What sites can we visit
from there?
There is enough to see for at least 2 full days in Bologna itself, possibly more. Parma is fantastic and IMO a must-see. Ferrara is nice, but don't go on a Monday when the castle and most restaurants are closed. those are the only places in the region I've personally been, but I have read and heard that Modena and Ravenna are both nice day trips. All of these are very short and inexpensive train rides from Bologna.
May I make a suggestion. I have been to Italy quite a few times. I went to San Gimignano-City of Towers this time around and loved this beautiful town. There is Florence with it many museums and the Basillica di Santa Maria del Fiore. Siena has a great amount of charm and lovely to walk around.
Do get Rick Steve's book on Italy with so many helpful ideas. One of my most favorites is Cinque Terre. Enjoy your trip. I love Italy!!
Ravenna is an easy drive or train trip away, and contains a number of churches and other buildings that contain amazing mosaics, dating back to the early days of Christianity. Those mosaics are in my "Top 10" list of man-made sights I have seen in my life.