Heading to North Wales

Chester is slightly more than an hour from Conwy while Caernarfon is about 15-20 minutes from it. Chester may have more places to rent a car, so that could be the deciding factor. The drive from Chester to Conwy is easy. Conwy is about 2.25 hours from Aberystwyth. It too is an easy drive.

There is no main line railway station at Caernarfon- only the Welsh Highland Railway steam train station which it would take you a two day journey from London to Caernarfon via that route.

In any case Caernarfon is beyond Conwy, so it wouldn't be sensible to overshoot and then to return the way you just came.

At least at Chester the main car rental companies are outside the city centre, and if you head for Shotton out of their yards you have time to get used to the car before joining the A55 expressway.

The most logical way would be to stay on the train to Llandudno Junction and rent from Enterprise there (it is a mile over the bridge from Conwy.
I don't know where you are going to after Aberystwyth as not even Enterprise have a depot there (just a car club). Shrewsbury seems to be the closest. This is an area where people either use their own car or use the very adequate public transport.

Unless heading to Northern England it wouldn't make sense to return to Chester or Llandudno ti return the car.

You'd be best continuing on the train from Chester to Llandudno Junction like isn31c said - there you can rent a car at either Hertz (opposite the station) or Enterprise (a very short walk). Llandudno Junction is minutes from Conwy.

You could even drive back to Llandudno Junction from Aberystwyth and drop it back there.

More time on the train, less driving, more relaxing!