I would suggest too having a think about time of year of the visit — 1. the weather, east is generally drier and sunnier, best time of year here for better weather is usually June though Feb can also be good; 2. some of the places noted above, Kerry, Burren, etc all very nice but very touristy and can be busy especially in the summer.
Less visited counties but very scenic are Leitrim, Sligo and Fermanagh–good for outdoorsy stuff too.
If walking is your thing, note there is no public rights of way network in Ireland, north or south, but cycling is great, as there are loads of minor, very quiet roads and tracks, for this the Ordnance Survey map is your friend :-)
https://dash4it.co.uk/catalog/category/view/s/os-explorer-maps/id/50/
https://dash4it.co.uk/catalog/category/view/s/os-explorer-maps/id/51/