Almost all of the roads along the West Coast bring you to fantastic places. The Wild Atlantic Way loosely ties a lot of them together.
There are only a couple of roads around Connemara (Galway / Mayo). Good places to visit in the area are Roundstone, Clifden, Letterfrack, Killary Harbour and Westport. North of Clifden watch out for Omey Island which you can drive on to at low tide. South of Clifden drive to Ballyconeely and keep an eye out for back roads leading down to loads of small beaches with crystal clear water and incredibly white sand. Like the Carribean except freezing.
If you want Wild try the road to KEEM beach on Achill island in Co. Mayo about an hours drive beyond Westport. Achill Island is reached by bridge. The narrow road is west of all of the settled parts of the island and climbs to around 600 or 700m above the Atlantic with no guard rail before dropping down to KEEM beach where there are no houses just a car park.
If you need somewhere to stay Pure Magic Kitesurfing in Achill have a B&B that is run by a bunch of French guys who refused to go home.
If you do end up in Donegal the road through the poison Glen at the foot of Mount Errigal is another wild spot.
Enjoy the trip !