Basement layout can be done in many different ways. Like in your case, you have lots of columns so you have to see which columns can be left exposed and be part of a room detail and how many columns you can hide inside the walls, etc. Here is an example of few basement designs I did for customers with a bit larger but similar needs, play area, media area, gym, etc.

When it comes to basements best if the design in 3D this way you can actually be inside of it as it was already finished, visualize everything while doing a walkthrough and see if that is exactly how you want everything to look, and you can make changes trying different options instead of trying to figure them out during construction stage or guess how it will look when looking on a 2D drawing.