Hi Trisha,
Claremorris is pretty central. Not sure if you are interested in Golf but, if yes, there are two great courses close by- Claremorris itself and Ballinrobe. In terms of sightseeing, the grounds of Ashford Castle in Cong are about 20 mins from Claremorris and are well worth a visit. You can even eat in Cullens at the Cottage in Ashford's ground- much more laid back than the castle itself and a lot easier on the pocket!
Westport's also worth a visit and you could take a spin out to Croagh Patrick and one of the many beaches (e.g. Bertra) while there... i'm ignoring the weather issue. Westport's ca. 40 mins from Claremorris The Tavern Bar and Restaurant is a good stop for lunch. It's on the Left hand side of the road when driving from Westport to Croagh Patrick facing the bay.
Depending on how much time you have, you could also take a spin on from Westport to Achill Island (another 45 mins from Westport). If you get a clear day, Achill is amazing.