This year the House of Welsh is undergoing another transformation: New owners are spending nearly $1 million to convert it from an old-time tavern and steakhouse to an upscale dance club and lounge.

The landmark building, which had been facing demolition, has now been reconstructed ‘as it was in 1915’ – but this time in St Fagans National Museum on the outskirts of the city. The open-air museum ...