Anyplace by the docks is great, especially at sunrise. Dingle town has some good pubs, too. Try McCarthy's, a block off the main street, for some true local flavor and some good interiors.
Dingle Bay has a resident dolphin, Fungi, who is usually very active. Look for the lighthouse at the mouth of the harbor and find your way out there in the afternoon (ask at the aquariumif you need to-very helpful)- there is a group of people surfcasting or boogyboarding out to play with the dolphin that makes for good photography.
The Dingle peninsula is possibly the prettiest, most unspoiled place in Ireland (other than Connemara), so anywhere you go has possibilities. The beach at Inch is also remarkable.
If you can go in by the Connor Pass. I can guarantee that you will spend half a day on that road if the weather is good-beautiful all around. If it's a nasty day, it is the worst road in the world.
Slainte