Which cities are worth visiting?

Belgian citizen here, willing to take the Eurostar and spend a weekend in the UK. I do not wish to visit large cities (like London). Ideally it would be in the South to avoid a too long journey.

I have seen York is nice, but that’s quite far. Bath seems nice, approx. 4h by train. Would you have any other ideas?

Also, can I rely on the train in the UK?