I know that Welsh property is cheap compared to other parts of the country, but £60k isn't a lot, even here. There will be rural (probably VERY rural) fixer-uppers for that kind of money, and quite possibly ex-council places in some of the more blighted parts of the country, but you won't get a lot for your money. It might be worth looking at places in the Valleys, particularly as there are moves afoot to massively improve rail infrastructure in some of them, which could mean you were buying in at the bottom of a potentially improving market.
A lot is going to depend on things like work - obviously, places with lots of employment tend also to be more expensive, and conversely, cheap places will also tend to be places without much in the way of employment opportunities. Something else you will need to pay careful attention to, especially if what you do requires good Internet connectivity, is the availability of decent broadband at an affordable price - outside the cities, broadband coverage can still be quite patchy, with either no, or only very slow, connections available. That should improve over time, but this may not be soon enough for you.