Ireland in Late November

I went in November last year, a little earlier but not much, from November 11-18. I'd say the weather was a mixed bag, with mostly clouds, temps in the 50s, although there was one particularly ugly day in the 40s with lots of rain and one particularly beautiful day that was 60 and sunny.

I didn't rent a car, because I didn't go to the smaller towns, but I highly recommend ditching the car when you are in the larger cities. I don't know if you are American or not, but driving on the opposite side with a manual transmission seems challenging enough without adding in the traffic of the city. If the anxiety of driving is too much, there are tours leaving the cities to visit the outer places, such as the Cliffs of Moher and Giant's Causeway. While driving is probably the best and easiest way, it isn't mandatory.

What cities did you visit? Did you travel by bus at all? Did they seem plentiful, or does it just depend on if it is a major city or not?

I went to Belfast and Dublin. Most of Belfast is very, very walkable, but city buses run frequently. Many tours leave Belfast to the Causeway daily.
Dublin is also walkable, with an easy-to-understand tram system going to further out places, like the Guinness Storehouse and Kilmainham Gaol.

Per Emily, having a car in the cities is more of a hassle than it's worth. For such a short trip, and given the likelihood of some pretty crummy weather, your best bet might be to base in one or two cities (Dublin, Belfast, Galway, etc.) , using public transport to get around and booking day trips to attractions that appeal to you.
Galway, for example, is a short train ride from Dublin and once there you can book day trips to the Cliffs, the Aran Islands, the Connemara Loop, etc. Likewise Belfast, which is about two hours by train from Dublin, from where you can easily book day trips to the Causeway Coast.
The public transportation systems in Dublin and Belfast are really quite good, and for extended stays there are multi-day passes that will make it a cost-efficient option for the two of you.
Safe Travels

I've been Ireland in November once and October once (and three other times in summer).

The advantages of visiting Ireland in fall are small lines at tourist sites and in accommodations. There are few other travelers. (I was the only guest in a youth hostel in Lisdoonvarna for the October visit.) I would say it's a good idea to take advantage of the smaller crowds by spending a lot of time in cities like Dublin, Cork and Belfast. I've rented cars twice in five trips to Ireland. They're good if you're going to remote areas, but the Irish bus system is efficient and reliable for everywhere else. If you do rent a car, drive slowly, remember right turns are hard and left turns are easy, the driver is always in the center of the road and to proceed slowly through the roundabouts. As far as the weather, I'm not a good person to ask because I'm from Chicago. Ireland strikes me as relatively mild in comparison. If you go to the Cliffs of Moher, there should be plenty of B&Bs in either Doolin or Lisdoonvarna.

Want to do something adventurous? Think about climbing Croagh Patrick, the holy mountain of Ireland, in Westport, Mayo. It takes 2.5 hours, and you'll feel that you accomplished something few others do. Start on the trail in the morning, as the sun will be down by 4 p.m. in November. Have a great trip.

There is extensive bus service between towns, as well as numerous local day tours that you could take to places like the Cliffs of Moher. www.buseireann.ie has a journey planner that should be a great help in figuring out your itinerary. I have rented cars in Ireland four times with almost no problems (one tiny accident - broken side mirror). You can adjust pretty quickly to driving on the other side of the road. But if it makes you nervous, you should be able to get to where you want to be via public means.

Craig I love your comments about Chicago weather vs Irish! My husband and I are planning a trip to Cork; probably looking at the week of Nov 18 through Nov 25. This will be our first trip to Ireland--we're very excited. We both have ancestry in County Cork. We decided to just fly in and base ourselves in Cork. We don't plan on renting car. From what I've read online it seems to be a city offering lots to do and see. We will probably visit Cogh and also we're planning to visit the Jameson Distillery; and also the monument to the Native American Choctaws, as I am Choctaw. Anyone who's familiar with Cork, please chime in on your favorite things to visit, music venues, pubs etc. And yes weather tips are welcome too.

Nick, I'm noticing that you are based in Tampa (I spent a couple of years in Clearwater)
I toured Ireland in late October.......a little drizzly, and cool temperatures (50s and 60s were daytime highs) but this is what I'm used to, having spent most of my life in the Midwest.
I think it is entirely doable for the two of you, but don't skimp on outer wear and dry socks!! (esp. around cliffs of Moher or giants causeway)