First, welcome to Nova Scotia!
Whiteymorange has covered most of it off on a provincial level. If you have more than a couple days, Cape Breton is worth the drive to see the Cabot Trail, Highlands and Bras D'or Lakes. That'll require a car, four or five hours of driving, a hotel, and at least a few days to explore.
The Bay of Fundy and its tides certainly are a sight to see. It doesn't matter which coastal road you travel, there are many, many villages along the way.
As for the downtown peninsula (where I live), it's mostly about the history of the place. Lots of 19th century buildings; old cemeteries; nice Victorian public gardens; colourful houses; the Citadel National Historic Site overlooking the downtown; and of course, the harbour with sailboats, container ships, navy ships and anything else that floats. There are a few universities downtown (including the Nova Scotia College of Art and Design), galleries (you'll be a couple months early for the large Leibovitz exhibit recently gifted to the Art Gallery of Nova Scotia) and other places to wander when it rains (because if this spring is any indicator, it will rain ... a lot). You could take a whale watching boat out to the ocean if that's your thing.
And of course, lots of places to drink and eat. People here *love* to go to the pub.
As with most things tourist-related, there's a website for that: http://www.novascotia.com/en/home/di...ovascotia.aspx
Hope that helps. Fire me off any questions you have, I've lived here six years now and have explored much of the city and province.