I don't know anything about the B&B you mentioned (Michelle will be able to offer better advice about accommodations than I can), but Parnall Square is at the top of O'Connell Street, so walking to the city center should be fairly easy (I stayed off of O'Connell Street just a few blocks closer to the Liffey than Parnall Square).  You'll come down O'Connell Street to the Liffey, cross the bridge, and to your left (east) is Trinity College and on your right (west) is the Temple Bar area. 

As for what not to miss in Dublin, that depends on your interests.  For me, Kilmainham Gaol was a must-see.  Lots of folks like the Hop On-Hop Off bus that hits most of the sights.  You can get off at places that interest you and then catch a later bus to continue your tour.

You would be staying close to the Dublin Writers' Museum (it's also on Parnall Square) and you'll pass the Garden of Remembrance and the GPO as you head down O'Connell Street. 

Have a great trip!