Americans would typically say they're going to the 'Mall.'
The 'Mall' would represent often a large number of different shops, usually grounded with two or more major department stores at either end, then dozens or hundreds of other shops, and 'food courts' in-between.
Have a look at these links for some ideas of how these 'malls' look. The term 'shopping centre' might also be used...although the americans would spell centre as center.
There may also be a cinema in the mall as well...but the americans would usually say the 'movies' or theatre...
http://www.simon.com/mall/default.aspx?ID=207
http://www.parkmeadows.com/html/index13.asp
http://www.mallofamerica.com/
I hope this was helpful. Best regards
Fr. Bill
http://www.projectnewlife.org