Leeds (25 minutes by train) — the regional capital, with the Leeds Art Gallery, the Victorian covered markets, the Victoria Quarter arcade, and a lively food and drink scene. Easy half-day or full day.
Wakefield (10 minutes by train) — a short hop that punches above its size. The Hepworth Wakefield is one of the best dedicated sculpture galleries in England, and the Cathedral quarter is worth exploring. The Yorkshire Sculpture Park, with its outdoor Henry Moore and Barbara Hepworth installations, is a short drive from Wakefield.
York (around 1 hour by train, changing at Leeds or direct) — the most complete medieval city in England. The Shambles, York Minster, the Jorvik Viking Centre, and the city walls reward a full day.