I would say that if you decide on the West, you should definitely include Conamara and at least a drive through southern County Mayo, by Lough Mask and/or Lough Corrib. There is an international airport at Charlestown in County Mayo with flights to Luton, Gatwick and Stansted and another outside Galway with flights from Luton and Southend.
There is some good walking in Conamara and it has a beautiful coastline. It is also a great area for cycling - if the weather is kind to you. If you want hiking in mountainous areas, Kerry is probably a better choice, although there are some very good hikes in the Twelve Bens in Conamara as well. You might want to order this excellent book and have a look through it before reaching a final decision.
On the whole, I would be inclined to say that it depends a lot on what you like in terms of scenery. Windswept rocky shores, half-barren mountainsides and surprising lakes - go to Conamara. Lush, hilly green landscapes and steep peninsulas jutting out into the Atlantic - you will find these in Cork and Kerry.
As for historical sites, there are several old ruined monasteries in County Clare, there is of course the prehistoric fort of Dún Aonghusa on Árainn, and Conamara is the strongest remaining heartland of Gaelic language and culture in Ireland - though there are also Irish-speaking areas in west Cork and Kerry. In West Cork, Gougane Barra or Guagán Barra is a very scenic early monastic site, even if there is not much left to see there. If you go to the south and the weather permits it, you should not miss a trip to Sceilg Mhichíl off the coast of the Iveragh peninsula.