First, you can't get from Clifden to Inishmore (or anywhere) by ferry, if that's what you meant (but maybe not). The larger ferry to the Aran Islands departs from Rossaveel, on the coast 23 miles west of Galway Town (www.aranislandferries.com/index.php). The smaller one departs to all three islands from Doolin (www.doolinferries.com).
With distances in Ireland so short, you shouldn't have to choose between Connemara and Inishmore! But if you're squeezed for time, I'd pick the former. If you do visit Inishmore, don't miss Dun Aengus!
With three overnights before heading down to Dingle, I'd suggest the first night in lively Galway Town, then drive the N59 circuit around Connemara (counterclockwise) the next day, stopping in Clifden for the night. There's some interesting history - not to mention the Sky Road - there. From Clifden, head to either Doolin or Rossaveel for the ferry to Inishmore for the third night. Once back on the mainland the next morning, you can visit the Cliffs of Moher en route to Dingle.
Or alternatively - especially if you want to listen to some of the best traditonal music in Ireland (four pubs, all within walking distance of everything) - overnight in Doolin, then do a day trip to Inishmore the next morning. In Doolin, I recommend the Fisherman's Rest B&B just behind O'Connor's Pub. Danny and Mairead are grand hosts. Their website is: www.accommodationdoolin.com/
With either of the preceding, you're seeing and experiencing more as opposed to returning to Galway Town each night.
My stays in Galway Town were always in a B&B near the university (a 15-minute walk to the city center) that's sadly no longer in business. There are plenty of wonderful B&Bs to be had (all over Ireland), many located on the road leading from the town center to Salthill, as well as near the university.
If you'd like a B&B recommendation in Dingle Town, let me know. The one I've stayed in a few times is in a quiet setting, only a five-minute walk from the town center.
With your itinerary, you'll be seeing the most beautiful region in Ireland. No matter where you go there, you won't be disappointed!