The biggest and coolest Bass Pro shop in the country! It has several wildlife museums in it IIRC.
http://www.basspro.com/webapp/wcs/s...gId=10051&langId=-1&appID=94&storeID=15&tab=3 ("Our store is almost 500,000 square feet in size making us the largest Bass Pro Shops in existence!")
There are fabulous walking paths all over town through residential areas and the ones I walked on were very well kept up and pretty ideal IMO. Also, walking in the Nature Center just south of town is fun. Take a camera because you will see some beautiful Ozark wooded scenery too.
Visiting nearby caverns! There are many, including Fantastic Caverns just outside of town on the north side. That's not the biggest or best caverns in the state, but it sure is close. If you want something bigger, get on the interstate and drive to Onondaga or Merimac caverns but they are farther away.
How about historical things? There was a huge Civil War battle at Wilson's Creek Battlefield, just to the SW of town.
http://www.nps.gov/wicr/index.htm
Fishing! Wow, go visit Stockton Lake. I think you can rent a boat there too, although you might want to inquire since my memory is a bit rusty on that.
Branson is nearby if you like that sort of thing.
There are several universities in town so you could visit them and wander through the libraries or attend cultural events there and so on.
There is a small zoo (in Doling Park, I think?). I think it is underwhelming but then I haven't been to it in almost 60 years. It might be better by now.
Really, there is plenty to do there and it all depends on what you like.
https://www.springfieldmo.org/things-to-do