According to your hotel website, it is conveniently located near a Aircoach drop off. Aircoach is a bus that travels from the airport to the center of Dublin with stops at a few hotels. Costs about €8 per person.
Mespil Hotel Dublin 4 | Dublin City Centre Hotel | Ballsbridge Hotels
The website for your hotel also lists several to see, depending on what your interests are.
You can book Aircoach online using this link.
Welcome | Aircoach