Does anyone have reccomendation for a Long Term Care; possibly dementia for my father in Omaha NE @150 per dy?

What should we look for in a LTC facility for my father. He can't walk etc. . . but does have some cognitive skills. He can tell us when he wants to smoke, go to bathroom, eat. He is so fragile right now. We don't want to give up on him and really hope that by a miracle we can find a doctor who will work with him. So far there's been no luck.

Very unlikely you will find a dementia facility that will allow smoking. But it is very likely you can take him out for a smoke when you visit.
You don't say what kind of dementia. Most dementias are not reversible. There is no miracle. Usually best hope is to prevent dementia from progressing. There are several medications to help with slowing the progress of dementias. If it is from a stroke or circulation in the brain, preventing a blood clot or further clogging of the circulation to the brain is the best you can do. You cannot reverse the damage that has been done. Most dementias are progressive. Usually attempting to slow the progression is the best you can do.
I'd look for somewhere where he is stimulated. Activities that he enjoys, other men and women to talk with who still are able to communicate. Not good to place him where the residents sit around and do nothing or watch TV all day.
Visit the facility at mealtime. Is everyone eating or being helped to eat? Is the food appetizing? Most facilities will invite you to sample a meal. Visit after the evening meal. Is everyone put to bed by 7PM? Or are they up and engaged in something pleasant and stimulating to do?
Check out the last state inspection. It will tell you what the state inspectors found on their last visit.
My heart goes out to you.