As you can tell by my username I live in York (inside the walls). It’s a fab small city with some excellent secondary schools both state and private. Very very safe, easy to get around and you’ve got the North Yorkshire Moors, Yorkshire dales and some cracking places on the east coast within 30-70 mins drive. Brilliant train connection to London too, under 2 hours on generally reliable trains. The ring road isn’t great but it depends on where you work or need to get to every day of course! The city is well served with ultra fast fibre too.
sure, there are lots of tourists but it’s not unbearable and if you’re local you can enjoy the city all to yourself first thing in the morning even in the middle of summer. in the evening whilst there are bars and areas frequented by groups (stags and hens seem to have calmed down a bit in recent years) a good bit of the city around the Minster area remains civilised. Race weekends are busy but there’s a handful of those a year. There are 2 cinemas and 2 large theatres in town with a good variety of shows, plus some small theatre / performance venues, some incredible restaurants and plenty of pubs, independent shops, cafes and bakeries. You can live centrally and walk to all this if that’s something that appeals. There are supermarkets around the town or out at the retail parks which are within easy reach.
I’ve also lived in Sheffield, which I think is a tremendous city which has a very vibrant feel and which has done loads to regenerate.
We visit Leeds for more varied shopping and theatre sometimes and I’m not a fan, it’s badly laid out with an appallingly confusing road system. But I don’t know more about it as a place to live.
As with all such cities, there are opportunities to live in smaller and larger and nearer and more remote villages all around each - so it probably does need you to think about which city you prefer for yourself and take into account schools, commuting distances, and what else you want to be near when heading away from the city rather than decide on a random village somewhere and hope you like the nearest urban centre.