You'll struggle to see much of Yorkshire and spend a lot of time driving around if you try to do much of the things mentioned during a few days.
You could spend a week each in West, North, South and East Yorkshire and barely scratch the surface on what to see and do. I've lived here and have spent over 40 years having very frequent days out and holidays and haven't seen everything I want to.
You could probably try staying a couple of days somewhere south of Leeds and then a couple of days somewhere further north you might be well placed to see the Wildlife and Sculpture Parks first, possibly also National Media Museum in Bradford or Royal Armouries in Leeds. Lots of big parks and animal attractions like Cannon Hall Farm, Temple Newsham Farm, Tropical World Roundhay Park in this area too.
Then you could go up to the Forbidden Corner and Yorkshire Dales, perhaps combining with Harrogate and Knaresborough and/or Ilkley.
Bolton Abbey would be nice on way up that way too.
Then there's also Flamingo Land and over to the east coast, but you really need a separate holiday for all that.
There was probably some amusement about the thought of staying in Wakefield on holiday (the city centre is sadly quite run down), but with the Barbara Hepworth Gallery, Yorkshire Sculpture Park, Sandal Castle, Newmillerdam, Thornes Park, Cannon Hall Farm, another farm/country house attraction I can't remember, Pugnes, Nostell Priory, Wentworth Castle, National Coal Mining Museum all very close to the city, plus canal walks and several smaller country parks and an indoor waterpark not far away in Barnsley then lots more to do in Leeds and further afield, I could think of a lot worse places to go on holiday and it certainly would be one way to have a holiday in a new place and also one that will be far away from the crowds of more popular places like Devon and Cornwall this summer.