Itinerary help! Ireland/N Ireland

I appreciate you're wanting to get an early start for your hiking adventure, but having a car in the city is a huge PITA. I would try very hard to get an early morning pickup instead. There are car rental offices all over. You just need to find one with early hours. Even if you pick up at the airport, at least it's on the way to where you're going.
For Giant's Causeway, I like Bushmills. We had a townhouse with parking just outside the village.
Derry is great. You can walk the walls in an hour if you're not stopping to read all the plaques. Be sure to visit the Museum of Free Derry (and do read all the plaques) before going to see the murals. Parking at the mall is reasonably priced (as I recall; it's been a few years) and gives good access.
Instead of Donegal, look at Killybegs, from where you can easily see the Slieve League from both land and sea. Best fish and chips of the trip came from the chippie in the alley across from Anderson's Seafood Restaurant (we stayed in an apartment upstairs). So good!

I think this sounds like a lovely trip. For the Mournes, I would look at staying in Newcastle- it's got a beautiful location right on the coast.

Hi folks, I am from Northern Ireland, so feel free to ask questions, so first off you will be driving in two different countries
Ireland (Republic of Ireland) and the United Kingdom (of which Northern Ireland is a part of) Ireland drives in Kilometres per hour
Northern Ireland the UK as a whole drives in miles per hour, road markings and road signs on both sides of the international frontier are different below for your info i have posted the links to the British highway code for Northern Ireland please read it,
then i have posted the link to the rules of the road for Ireland , second thing i wanted to say was it is now required by British law for every visitor to the United Kingdom to get a ETA, this is not a visa, US citizens can enter the UK visa free for 6 months, but this is required to cross the UK/Ireland border into the UK, people will tell you it is open (which it is) and you dont need one (which is incorrect) there have been an uptake in authorities on both sides of the border doing spot checks at various locations inside their own juristictions so make sure you have a valid ETA for the UK
also currency wise it will be pounds in Northern ireland not euros
have a safe trip
links :
https://www.gov.uk/eta/apply

https://www.nidirect.gov.uk/articles/highway-code

https://www.rsa.ie/docs/default-source/road-safety/r1---rules-of-the-road/ruleoftheroad_book-for-web.pdf?sfvrsn=b5d57830_7

Thanks for your responses so far! I appreciate all the tips - have downloaded the UK ETA app and getting those in order is top of the list.
In the meantime, I've actually tweaked the itinerary to include some of your helpful info and also go the opposite direction - now looking at
day 1. arrive am to Dublin, explore Dublin, evening yoga class in Temple Bar, adjust to time difference

day 2. keep adjusting to time change, more Dublin, likely Guiness tour (husband's request). stay in Dublin.

day 3. pick up rental car & depart first thing am for Sligo - longer drive but looks like mostly larger roads. Stay in Sligo.

day 4. Head to Sliabh Liag - explore by foot or possibly boat. Stay in Donegal town.

Day 5. Drive to Derry, lunch & walk about to see murals, etc. Drive to Giant's Causeway & hopefully Carrick-a-rede rope bridge. I'm thinking we might be able to time the Causeway visit to miss the tour buses but don't want to miss out on the rope bridge being too late. Stay at a glamping pod just south of bushmills.

Day 6. Drive to Newcastle - depending on timing/weather/energy levels, crash & rest or do some Mourne hiking. Stay in Newcastle.

Day 7. Depending on prior day, do some mourne hiking. Head back to Dublin, I'd love to slightly detour down to Carlingford Lough to take the ferry on our way. Stay in Dublin. We might actually be meeting up with some friends from home for dinner! TBD if return rental car on our way back in & taxi to airport in am? Or keep car & drop at airport pre-flight. Flight scheduled for 10am - would love any insight on that piece!

That sounds really nice, and recommend the Carlingford Lough ferry- I think you could fit that in pretty easily. If you need a place to stop along the way- we stopped for lunch in Annagassan once where we had a great view of the ocean while we ate. Of course you will also be passing near Bru Na Boinne on your way down to Dublin, but not sure if you will have the energy to fit in something else!

After or before the rope bridge, definitely check out Ballintoy Harbour- one of the most scenic parts of the Causeway Coast in my opinion- also stood in for the Iron Islands in Game of Thrones.