How to give Dad in NH a purpose?

Put him to work writing his memoirs. There are a lot of books you can get with prompts to give you ideas of what to write about, and even random memories are invaluable to the younger generations to help them understand both him and how life used to be.
My dad started writing his memoirs when he was in a club. Each week, they'd take turns telling a little bit about their background and upbringing, so he made a few notes. Eventually that expanded to 18 typed pages of stream of consciousness memories, and it was priceless. There's so much we don't know about our parents' lives, and even if they think something is boring and inconsequential, it often isn't.

One of the last things my Dad said to me was, "Did I write down that I once danced with Keely Smith?"

Yes, Dad, you sure did.

Can you speak to the admin to see if he can have a position as some sort of assistant or ambassador within the facility? Perhaps the people who manage the activities can use help in preparing things (organizing, cutting, sorting, etc).

Many years ago my son's daycare had a lady come in weekly -- Gramma Pat -- and she lead story time hour by reading the little kids a book. She was very elderly but did this for many years. They loved her visits and we remember her to this day (30 years ago!)

My mom used to volunteer at our town's senior center and they had a group of ladies who would collect holiday or occasion cards, cut the fronts off and reglue them to a new blank card. They would package and resell the cards so that the proceeds went back to the senior center.

My own personal favorite is cutting old t-shirts into rags. Went through a through a ton of rags when my boys were all home and we certainly had plenty of crappy t-shirts. There are "circular" cutters that cut fabric but are easier on arthritic hands. Collect old t-shirts from neighbors and give them to your dad to cut (if he can). Then he can bundle them and you can help distribute or sell them in the community or even within the facility. Home Depot sells boxes of rags, so they're definitely needed!

Caringchild, does dad NEED NH level care? Is it possible that, with his improved health he might be more suited for an Assisted Living facility?

If he needs NH level care due to health issues, bring this up at the next care meeting-- get the Social Worker and activities director to find a job he can do.