If you must go to Moher go very early in the morning or very late in the day. They are beautiful but tourist overrun, clogged with tour buses, tacky gift shops and traffic. There are many better Cliff sights in Ireland....far more the windswept, rugged "lonely" cliffs people dream of.....like the Cliffs of Kerry, Slieve League, Cliffs of Kilkee and the cliffs at Dun Anghosa to name a few. Moher is pretty just way too touristy. To avoid some of it take the cliff walk there off from the hubbub at the visitors center. Very pretty.
Skip Blarney. It's on Rick Steves top ten tourist traps in all of Europe. The castle grounds there are fairly pretty but there are dozens of prettier castles with real history attached.
If you stick in the West there is plenty to fill months let alone 9 days. Try and avoid too much driving. The goal should be to experience Ireland - it's incomparable beauty, amazing history and the warmest, funniest most welcoming people you'll come across.....So linger, explore and don't fall into the trap of running all over trying to see everything ....it's very self defeating.
Not sure what your interests are but Connemara near Galway is pure heaven. Dingle and the Slea Head drive is incredible. The Aran islands are gorgeous with wonderful scenery. The Ring of Kerry and the Skellig Ring are incredible. The sights near Killarney (not the city itself) are awesome....Gap of Dunloe, Ladies View etc.
If it were me and I was trying to see a lot without overdoing it I'd stay in the west....a few days near Castlemaine or Kenmare area and see the ROK and Skellig areas. Then a day or two in Dingle and then perhaps Connemara. Ambitious enough and still a lot, possibly too much driving but you would get world class scenery, amazing history, great food and music and a real sense of wild Ireland.
With limited time I'd avoid going East to Dublin....you lose days in the car. But if you do go there try and see Glendalough and Newgrange as day trips. But honestly I'd stay in the west. Enjoy, you'll have a great time there....it will be busy, peak tourism but is doable !!!! Best of luck.