Yorkshire tourism mostly equates to the Dales and NY Moors national parks, the seaside places, plus Leeds and York. The Yorkshire bit of the Peak District is not included in 'Welcome to Yorkshire' as the Peak park 'belongs' to Derbyshire in tourism terms. Sheffield has a bit of visitor action but not that much really, we can do better..
In terms of positioning or branding or place marketing, it's fine to have a few different images for a city, they're never simply defined by one thing. Being 'Steel City' was never an adequate definition. We're definitely a music city, definitely an outdoor city. Other things we can do better (retail, museums, stuff to do when it rains, food etc).
In the UK there is London, which is a global city. Then there are the big cities/regions Birmingham, Manchester and Glasgow. Look at where bands play if they only have a handful of dates in the UK, it's these places. The next rank is the regional capitals (eg Leeds). Then there is Sheff on the next rung..That's where we are and it's fine. All we can do is make Sheff as good as it possibly can be. We can close the gap on Leeds by being different and better in some ways, like Liverpool does with Manchester. But I doubt we can ever 'get promotion' to those higher levels of economic and political importance.