I started an Accelerated BSN at age 53 and graduated with an MSN (NP) at age 56. I got hired within 2 months of graduation. But it sure was hard! I was always a straight a student and the ABSN was the hardest academic program I have ever done. See how you do on your prereqs. I do know a woman who started med school at age 65 and she did ok.
There will be some age discrimination, but there will also be plenty of employers who won't care. There are some 60 somethings in great physical shape. Most hospital nursing jobs are very physically demanding. However, there are nursing jobs that are not so physical - psych, school nurse, public health nursing, case management, etc. Be honest with yourself as to your physical capabilities. Also, if you work in an underserved area or with an underserved population, age discrimination won't be such a factor.
There are scholarships
available, so the total cost will depend on the school you go to and the financial aid you receive. Johns Hopkins is expensive, but over 70% of the students get scholarships and some are full-ride. Check with each school. Sometimes the more expensive private schools have better financial aid because they have huge endowments.