When I had a similar problem, I told mum that I would go and see one home every day, then visit her in hospital (by this time out of the acute hospital and finally at the hospital just a mile away) and tell her about each one in turn, what it was like, what the grounds were like, and give her a brochure for the home. It also showed the hospital that I was doing something about discharge.
Mum and I have similar tastes, she trusted me to tell it how it was, what the vacant room looked like, etc. etc. Then mum felt that she had some say in choosing where she wanted to be.
In the end the only vacancy when she was finally ready to leave hospital was the best one in the area less than 2 miles away. Especially good news as one of the directors of the company that owned it is my next door neighbour. I "accidentally on purpose" mentioned this at the home one day, I'm sure this helped mum get good care at times!! Every so often neighbour would ask if mum and I were happy with things there.