Like your Toronto wuestion, it really helps to do some of your own basic research and also let us know your interests. Most of the key sites are already well covered on numerous websites so using Google will help you get started. Regardless, the basics are:
Strolling downtown and the waterfront
Chez Piggy is the most famous restaurant and deservedly so. There are many excellent restaurants.
While not 'unique' there is a very good bakery (with an attached cafe), called Bread and Butter (Toast and Jam). If you want to pick up something sweet, it's worth a visit. http://www.breadandbutter.ca/
While not available every day, you may be interested in a tour of the Kingston Pen
I worked one summer at the Pumphouse Steam Museum many years ago. It's very small but can be interesting if you have a mechanical mind. https://www.kingstonpumphouse.ca/
If you are birders or love an evening walk in the woods etc, consider Lemoine's Point.
Those are the only "local" ideas I can think of. The big stuff is pretty well advertised on the Kingston website. (Fort Henry; Sir John A MacDonald's home; the waterfront)