Check out this thread with a walking tour of Nassau.
It has all the sights within a few blocks of the port area.
We did this walking tour twice in the past year and loved it.
You could easily either get a cab to drive you to the sights for a few hours or catch a horse and buggy right at the Welcome Center and they will go to the sites also.
I personally recommend to not miss the view from Fort Fincastle and the beautiful Queen's Staircase and it's waterfall, just below it. (have your driver drop you off at the bottom, by the hospital, so you don't have to walk the 66 steps)
The Graycliff hotel on the tour has amazingly beautiful grounds (looks like a hotel you'd see in the 1930's or 40's Hollywood) and a beautiful house converted to a restaurant and hotel.
The Government House (the big pink mansion on the hill when you dock) has a great view from the street looking up the massive stairs, with a statue of Christopher Columbus.
The beginning of the tour, Rawson Square, Parliament, the Supremem Court and the Library (old jail) are all literally right out the Welcome Center straight ahead and to the left a bit.
I haven't been to these two yet, but we are planning on going to them in September.
Fort Charlotte is just past the British Colonial Hilton heading west towards Cable Beach. (the British Colonial Hilton is the huge hotel just to your right when you dock)
Ardastra Zoo and Gardens is just up the hill from there.
Here is a link to their website to see if you think she might enjoy it.
(plus in the directions, it shows you Fort Charlotte and how close they are to the port area)
Hope this gives you a few ideas of things to see in wonderful Nassau.
(just steer clear of Bay Street and the overcrowded shopping area and the Straw Market )