Unless you have mobility problems I would anticipate walking virtually everywhere except the Gaol. The Storehouse is a little further out but everything else is within a couple mile radius. Dublin is a small city for the touristy sites and while we had an extra day on our bus and tram pass we never actually had occasion to use it. I would be surprised if taxis weren't tightly controlled in the city but the traffic in Dublin could make even small distances expensive by taxi and I would plan on using public transportation. I would just spring for the tourist transit pass and use it if you feel like it.
We saw Christchurch, the Dublin Castle, the University, the Archaeology Museum (amazing BTW), the Irish heritage research center and all the other sights just walking around. The great thing is we also stumbled across interesting places and really got a feel for the city. We didn't see the Gaol but everyone says it is well served by mass transit and easy to get to.
I realize I didn't answer your question directly hopefully that helps.
Have a great trip,