I took 6 months of parental leave in 2017, and got to be at home with the Chap* from 6-12mos. I found that I had tons of free time in the first 3 months, then less so as the months passed. He started crawling at 8 months and walking at 11, so those were the two big changes that affected my free time since he needed more attention once he was mobile. Here's what I did to pass my time:
-Cleaned the house literally every day, and had dinner ready when the wife got home (this was mostly to just to see how difficult it would be to maintain for 6 months...it wasn't....at all)
-Worked out almost every day in the home gym (and now I have several lingering injuries as a result, so maybe don't do this)
-Read a ton while he napped (usually 2-3 naps per day in the beginning, down to 1 or 2 by the end)
-Played lots of guitar
-Took him out walking every day if there was no rain
Basically, I had time enough on any given day to clean, cook, play with the Chap, exercise, and still enjoy my other hobbies. My game recommendation would be X-Com: Enemy Within (not sure if it's on Steam). I don't game as much as I used to, but I still love to replay that one every year. That and COD Zombies.
*Bonus points if you know that literary reference