Col Buendia - If you're in Aber for a day, I'd recommend going up to the Arts Centre for a look round as there's nearly always interesting exhibitions on up there, it's got a lovely cafe with stunning views over the sea/bay as the Centre's up on the hill leading out of town, it's got a very good independent bookshop and it's generally just a nice place to hang out! It's close to the National Library as well (about 5 min walk), which is also well worth a visit. It's got a very interesting exhibition of not only ancient Welsh books and manuscripts but also early English books by Chaucer and others, as well as some lovely paintings by Welsh artists like Kyffin Williams etc. The temporary exhibitions at the Library are also very good - they recently had a fascinating one about the history of popular protest in Wales, its been replaced by one about family trees/tracing family history which also looks really interesting.
The beach/seafront in Aber is also worth a stroll along, although if you're looking for a sandy/golden beach, its worth making the trip a little bit out of town to Ynyslas (about 5 north of Aber) which is a really lovely, long beach with miles of dunes and an interesting nature reserve. If you fancy a walk while in Aberystwyth, you could go to Tanybwlch beach, just south of town and from there walk up Pendinas, which is the ancient Celtic hillfort from which the town grew around, and enjoy stunning views of the bay ahead and the rolling hills behind.
Aber's very well served for cafes, pubs and non-chain shops. Until Costa recently crashlanded in town, there were no chain coffee places in Aber and the older cafes in town like the Cabin on Pier Street, are nice places to relax in if it happened to be a rainy day (not that it rains much in Aber of course!). For bookshops, there are two very good second-hand/independent bookshops in town as well as an excellent branch of Oxfam Books and a brilliant Welsh book shop which has a great collection of Welsh/Anglo-Welsh/Welsh-related books and CDs. Aber still has an independent record shop, Andy's Records (not the same Andy as the chain 'Andy's Records') which has some great sutff on CD and vinyl, lots of interesting box-sets and rarities. For pubs, there are at least 40-50 I think so no problems there! Some have gone a bit chainy/downhill in recent years but there are still some really nice ones like the Castle, the Ship and Castle, the Coopers/Cwps and the Black Lion. A little bit further afield, out of town, pubs like the Druid in Goginan (4-5 miles out of town) have a great atmosphere and do good food.
The actual castle in Aberystwyth is well worth a stroll around, although it was a bit ruined by Cromwell and his canons! It's a lovely place to sit and look out to sea on a sunny day. The nearby Old College building, which is where the University of Wales began in the nineteenth century and is still part of the University, is a fascinating building, and is usually open if you wanted to have a nose around. There are many other fascinating and beautiful historical sites in and around the Aber area, such as the Hafod estate (whose owner Thomas Johnes was unusually enlightened and visionary and whose guests inculded Turner and Coleridge) and Llanerchaeron (an amazing house designed by John Nash which has been preserved as it was when the last owner lived there in the 1950s and has really beautiful gardens), near Aberaeron.
So all in all, there's more than enough to do in Aberystwyth for one day!
Couldn't wait to get away.
