Tony has some great tips:  http://ireland.activeboard.com/t50055177/n59-galway-route/    

What I would do depends on your interests and determination level.     

Either of these would be long days in Summer.  In October you would need to be VERY particular about stops and visit times. If you want to see less and visit more, it might be best to forget Cong, the coastal route (R336) and maybe even Roundstone and the Inagh Valley and just trace and re-trace the N59.  

Some options ---

On one day, If you are into Coastal Scenic, try heading out from Galway on the R336 through Spiddal and Inverin, before it heads North, to Maam Cross and join the N59 there.  Just past Recess, turn South onto the R341 toward Roundstone.  Continue on, into Clifden, Letterfrack and Kylemore Abbey.  Return to Recess via the R344 (the Inagh Valley) and then return to Galway on the N59.  It could make a longish day and that might 'short-change' Oughterard and Moycullen.

On the next day, take the N59 to Maam Cross, but then turn North on the R336 and follow it to rejoin the N59 at Leenaun.  Shortly after, turn onto the R335 at Aasleagh (see the Falls!) and drive by Delphi Lodge and visit the Doo Lough Famine Memorial. enroute to Louisburgh, Murrisk and Westport.  The R335 is one of THE most scenic routes in Ireland.  From Westport, you could hop over to Castlebar and then either take the N84 back to Galway or the N60 to the N17 -- and the return to Galway. Another option is to return to Leenaun on the N59, then take the R336 back to Maam and connect with the R345, into Cong, before joining the N84, in Headford and following it into Galway.

Some other options/ideas:

Tony's map:  https://www.google.com/maps/d/viewer?msa=0&mid=1PzDDrrtHmP1sLhTs1AbrbcXjRx0

I think that the location of Killary Sheep Farm may work better with your trip. You can do Connemara in one day as long as you start directly after breakfast.