We'll be driving from Portadown with plans to ferry out to Inishmore and see the Cliffs of Moher the next day. Are we better off driving to Galway and seeing some of Galway and driving to Doolin the next morning or skipping Galway and taking a slower drive ending up spending the night near Doolin?.
What time ferry are you planning on catching from Doolin in the morning? You need to allow at least 90minutes to get from Galway to Doolin AND you must arrive at least 30 minutes before the ferry departure time. That could mean a very early departure from Galway.
Unless there is a very compelling reason to stop in Galway, I would plan to spend the night at Doolin rather than Galway as it makes for a less rushed morning.
The drive from Portadown to Doolin is going to take a good five hours PLUS any stops. Clonmacnoise might be a good midway stop. It is a lovely early Christian site on the banks of the River Shannon with ruined chapels , round towers and carved crosses. If you would prefer to stop in a town, then think about Athlone.
A bit further is Athenry is a lovely medieval town with ruined castle priory and remains of the Medieval walls - another possible place for a break.
Take the N67 roud the coast to Doolin. This takes you past Dunguaire Castle, Kinvarra (Ireland's answser to Scotland's Eilean Donan Castle!) to Ballyvaughan. If time allows consider taking the R477 from Ballyvaughan round the coast past Black Head, and Fanore to Doolin.