If possible, I'd highly suggest taking a bit of time to go through the north as well. The north coast is amazing and has several sites/sights that you won't find in the south. There are no border checkpoints/customs going from the north to the south and I've driven through without incident. Although many of the places I went are touristy, they are well worth seeing as you won't find many places like them in the world. Giant's Causeway is spectacular. If you arrive earlyish in the morning, you'll beat the crowds and have ample opportunity to shoot the scenes with no people. There are also the Glens; several steep short(ish) valleys that are full of water, greenery, and apparently fairies. Dunluce Castle (ruins), Mussenden Temple, and Rathlin Island are also all worth seeing. Also, Carrickfergus Castle is one of the longest occupied castles (built in 1177 and occupied until 1928) and worth a look.
In the Republic of Ireland, I tried to make sure I added some less touristy places to my itinerary. The Great Saltee Island is an interesting place only accessible by small boat (wet landing) but is primarily of interest to seabird photographers (particularly for the ability to walk amongst the puffins) and August isn't the time to see them as they typically leave at the beginning of the month. However, the landscape photo opportunities are still quite good and you will get photos that less people have. A very touristy place is the Rock of Cashel, and after doing some research, it appears that the buildings on the Rock are often being rehabilitated and don't make for good photos (full of scaffolding). And, being touristy, was nixed from my list. So, my research took me to an Abbey which is literally down the hill and purportedly had many less people. It did not disappoint. No crowds (barely any people), no admission fee and great photo opportunities. The place is called Hoare Abbey. Highly recommended.
I agree with others that the west coast is a very nice place, but as with most places in Ireland, beware the ever changing weather. I only spent a couple of days there and was stymied by a lot of cloud, rain, and fog that wasn't appropriate quality for good landscape shots. The Burren was great, but I didn't get any useable photos as a result of the weather. Another place I liked (from afar) was Dunguaire Castle near Galway. Not worth the price of admission, but the wide angle shots from farther back were great to me.
Others have also mentioned Glendalough, just southwest of Dublin. I agree that is an interesting place to visit, even if it is often jammed with tourist buses. Nearby is the Wicklow Mountains National Park. It was historically mined for peat and still shows the massive scars from that. It is truly a magical landscape and even though there are still some cars and other people, you do feel like you're very isolated (and you are). It makes for a nice drive and amazing landscape photos. You can do it in an afternoon, but it is more properly done in a day or two.
You mention Trinity College Library. GO. I can't say enough about this place. Seeing the Book of Kells and the other books was amazing, but the Long Room in the library just blew me away. All the old books and the colours of the wood were just phenomenal. The first time I was there, no photography was allowed. I was there in 2015 again and it is now allowed. Wonderful place and I highly recommend it. No tripods though. Take a good lens and high resolution camera body as no flash photography is allowed and it is heavily "patrolled". Be prepared to brace your camera on poles and other stationary, non-antique objects to get a sharp shot. Alternatively, don't be afraid to crank up your ISO if possible.
Take a look at my photo albums on flickr. Many of the shots aren't amazing but they are georeferenced and can also give you an idea of whether you'd like to add the places to your itinerary or not.
My 2015 trip:
https://www.flickr.com/photos/sgtsalamander/albums/72157656449404091
My 2012 trip:
https://www.flickr.com/photos/sgtsalamander/albums/72157629974849904
Good luck making decisions. It is an amazing island and you'll enjoy it no matter where you choose to go.
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http://www.flickr.com/photos/sgtsalamander
). I've found the vast majority of the Irish people I have met to be kind hearted and genuinely interested in making my trips as successful as possible. Ask your B&B host for help and sure he/she will be glad to provide it.