Hi, Norma. If you're getting a ride to the castle than don't worry about renting a car. There is probably a way to get there by bus if you really need to. Bus Eireann is the quasi-governmental bus company that would service that area. http://www.buseireann.ie/. There are some private bus companies that are very good but they usually only service places that have a great deal of demand to reach, such as Galway, Cork, etc. I don't think there are any that service County Cavan but I have never lived there so I cannot be absolutely certain. Either way, taking the bus would be less than ideal so it's definitely a good thing that you are getting a lift.
From what I can tell, there is no train line that services Kingscourt (where Castle Cabra is located). Irish Rail is the name of the national rail service. Here is their website: http://www.irishrail.ie/travel-informat … oute-maps.
For places to see when you're in Dublin, I'm not the best to advise on this because I only travel to Dublin for work and I don't like the place very much. That said, I know some places of interest. You should definitely check out (1) the Book of Kells (actually consisting of several books), which are kept on display at Trinity College (which just changed its name to some other similar iteration for no good reason). Trinity is right in the centre of the city, just south of the River Liffey (pronounced "Lif e"). Trinity is in Dublin 2 (Dublin is the only place to use area codes although they are bringing in area codes in the near future for the rest of the country). Dublin 2 is the nice part of Dublin. Areas north of the Liffey are generally not very nice. (2) Take a stroll down Grafton Street, which connects Trinity's campus to St. Stephen's Green to the south. This will give you plenty of places to shop. (3) Check out the tourist-attraction neighbourhood of Temple Bar, with its quaint old-Dublin architecture and cobblestone streets. Temple Bar is very close by to Trinity and in easy walking distance. (4) Maybe check out Dublin Castle, not far to the west of Temple Bar. Not sure what you can see there as it is the current centre of government. (5) Maybe check out Phoenix Park, where you can see deer roaming in this large central city park (best to take a taxi to get there). Taxis are plentiful and pretty cheap within Dublin.
I'm sure a Dubliner would be annoyed by my short list but that is all I've heard about the place.
One place you should definitely see about 45 minutes outside of Dublin is Glendalough, a mountain lake island where St. Kevin established a monastery in the 6th Century. You may be able to book a tour there from your hotel or some other service in Dublin. I've never done that so I can't be of much help. I've only visited by car. It's a very beautiful place.
Now, the absolute most beautiful part of Ireland is the West. But to visit there and be able to take full advantage of it you'd have to rent a car. Connemara is part of Counties Galway and Mayo and where people still speak the Irish language as their primary language. The landscape, with its rugged coast and stunning mountains, is strikingly beautiful and unique. Its villages and towns are unforgettable (for instance: Roundstone). It's easily one of the most beautiful places in the world. I could go on and on about the West but it doesn't look like you'll be heading that way so I'll stop here. Good luck!