There are many things to do in Dartmouth for every age level. I particularly love the MicMac Mall. It is four levels of shopping and restaurants, and if you go at Christmas time, you will have the honour of seeing Woody the Talking Christmas tree. The huge 100-foot or so tree will talk to each individual child, commenting on their outfits, etc. Marios restaurant is in this mall, and they have the most awesome food!
Dartmouth also has alot of history and great old graveyards. There are several museums and the downtown is very small but quaint. The ferry will take you over to Halifax and it is a very nice 10 minute or so ride.
Quick Tips:
There are kiosks in all the malls (Penhorn Mall, MicMac Mall, and the Dartmouth shopping centre) that have information on the area.
Best Way To Get Around:
Taxis are cheap here compared to other Canadian cities that I have been to. The public transportation is good, but the buses come once per hour most times. It can be fairly frustrating.