Out of all of those areas, I would choose Cuyahoga Falls.
Really nice especially around Broad Blvd. From what I understand, the area around Prange is not too great.
But other than that...I hear they have great schools (I've lived in Akron for 10 years now and I have no children but everyone I've known who lives in the Falls raves about the schools and the Police Department.
You might want to check the Akron/Canton section of Craigslist.com to see if there are any homes for rent (they usually include the Falls).
As far as renting a home...eee I would say between $650 at the absolute, absolute lowest (and that might be more of an Akron low) and on up.
Lots of shopping on and around Howe Ave. including Chapel Hill Mall (
Chapel Hill Mall - 330.633.1131 - 330.633.1131) which is your typical mall actually in the Akron limits, and big box retailers such as Target, BestBuy and Home Depot. Multiple sit down and fast food restaurants as well. This is CuyFalls' site - you'll notice that they have a lot of things going for the family especially down near the riverfront on Broad
City of Cuyahoga Falls :: Official Website
I always say that if I ever moved from downtown Akron, Cuyahoga Falls is the only other city I would want to live in in this area.
My second pick would be Stow, which is basically right next door to CuyFalls towards the north.Although I don't know anything about the schools, its a nice area.
If you like more of a country feel, with more land, choose Tallmadge. Its a safe and well taken care of community. I like the city, so for me, Tallmadge wouldnt be on my list.
As for nursing....there are several hospitals in the area. Summa is pretty big here
Summa Health System. They have hospital branches in downtown Akron & CuyFalls that I am aware of. There is also Akron General
Best Ohio Hospital | Akron Doctors | Best Ohio Healthcare - Akron General Medical Center which is in downtown Akron. Another big one is Akron Childrens Hospital, also in downtown Akron
https://www.akronchildrens.org/.
Hope all of this has helped a bit and it wasn't too overwhelming. I hope the links work as well. If you need any other help, just let me know.

~D~