If the weather is nice, take a walk by the canal and the Shannon up to the university (follow the yellow signs of the walking path to Lough Derg that start in the city centre). Don't miss walking the Living Bridge across the Shannon. You can continue to the Lime Duck (a little pub on the Clare side) and walk back on the Black Bridge. If you're tired, you can take the bus back into town!
On a rainy day, go and visit King John's Castle, the Hunt Museum and do a bit of shopping in Brown Thomas.