I'm assuming your neice is at a university is London itself, but has she done some traveling already? Presumably she may have an idea of what she wants to see - I know our kids do.
Our son was at university (Durham) in the UK and now works there, and on trips to see him (generally around Christmas time, so similar weather/daylight hours) we have taken him to Edinburgh a couple of times and York. Edinburgh would be a stretch coming from London for such a short trip, but York could work well. Closer to London, Bath is nice, ditto Oxford, Cambridge also.
All of these places work well by train from London and are cities, so the weather and limited daylight are not a big deal.
I think for you an easy train journey is the main thing, given your limited time. People do tend to warn about UK weather in winter, but it doesn't bother me, and we've quite often done countryside stays in winter - actually our first trip to visit our son at university was a week over Christmas and NY in the Cairngorms in Scotland. It was cold, dark and lovely. And we're planning next Christmas in Wales...