I'm a bit confused because the hospital has free on-site car parking.
https://www.spirehealthcare.com/spire-leeds-hospital/patient-information/about-spire-leeds-hospital/
So, as I see it, there's no need to look for a hotel that's particularly close to the hospital but simply one (with decent parking, etc) that's within a reasonable driving distance (of, perhaps, 15 minutes or so?) of the hospital. If so, that opens up far more opportunities than simply looking for a hotel in the immediate area of the hospital. On that basis, staying on the Weetwood Hall Estate (about 15 minutes drive from the hospital) might be a possibility:
https://www.weetwood.co.uk/
(It's worth searching online for rates which might possibly be cheaper than those on the hotel's own website, despite the 'best rate guarantee' shown there).
Similarly, the Old Coach House is only a 10 minute drive from the hospital:
https://www.booking.com/hotel/gb/the-old-coach-house-leeds.en-gb.html
(Parking is 'thirty seconds down the road')
Hinsley Hall is about 17 minutes by car from the hospital. (It's roughly in the same area as the Premier Inn that you stayed at before). It seems to offer everything that you want, at sensible prices:
https://www.hinsley-hall.co.uk/accommodation/