Sightseeing wise, the best the country has to offer is in the south, west and north of the country. Quieter roads then in the east as well. You can reach any part of the country in a day's riding too - so you've got plenty of choices. When you decide where to go - let us know and we'll point you to more specific spots and roads to ride (and what ones to avoid).
I just brought a group of 8 bikes / 11 peeps down around the Killarney (Co. Kerry) area for five days - with the help of some local knowledge from lads on here, we found some lovely back roads off the beaten track with some drop dead gorgeous scenery. The well known Ring of Kerry is only the tip of the iceberg - there's much much more to see...
Couple of years with back the same group we rode Dublin to Galway, then south through Co. Clare and the Burren, eventually staying three nights in Killarney. Happy to pass on the highlights of places we stopped and route we took if ye want...
If you go west from Dublin you'll get to enjoy Galway, Connemara, the Atlantic coastline. Also a bit quicker to get to than the likes of Killarney. Some great roads out this way too, good tarmac, little traffic and top scenery.
Further north you've got Sligo, and Donegal - again, lovely rugged coastlines. Fair few places of interest to see such as Glencar waterfall etc.
Lads from 'Norn Ireland' will be better versed in giving you tips for that part of the world, but the Antrim coast road, Bushmills distillery, Giants Causeway, NW200 heritage are all very popular with bikers.
Most important thing is to aim for quality not quantity - keep yer daily mileage low (average pace round here is slowish) and have plenty of time for stopping to see the sights/do the fun stuff. Oh, and sample the Guinness every evening along the way...