Don't go to Belfast!!! Or do but another time.
Lots of great ideas here, Howth or the Bray head walk are both lovely - I would pick one to do since you are getting similar views of Dublin Bay, just from different ends.
The Natural History Museum aka Dead Zoo is a great old fashioned museum. I was there a few years ago and they were filming a TV show there, perfect setting since it is all beautiful and old. (please tell me they haven't changed it too much since reopening...)
Other walks that are quite light and fun are the Sugar loaf mountain, and the Hell Fire Club.
There is a new treetop walk in Avondale in Co Wicklow (1 hour drive) with a giant slide. Lovely walk, although the lines for the slide were too long for us.
Giants Causeway, although nowhere near Dublin, is amazing and like nothing else I have ever seen.
National Museum of Ireland is worth a visit too.