I definitely would look for a children's hospital too. At least at the current place they are familiar with him and he knows the place. If you're able to, maybe offer for him to pick something out at the dollar store by showing him a picture of a dollar store.

If he has a comfort toy to bring or maybe bring one of his favorite treats to have afterwards. I hope it goes as well as possible.

We always have to schedule my son's blood work at the lab at the children's hospital in our area to get a blood draw on him. He also hates doctors and fights them.