I spend a lot of time on these forums, reading and posting, which has me searching scripture. I watch wholesome YouTube content that I can learn from. I get out and go run errands, or go to the park and enjoy nature (I'm retired). I do have hobbies which I rarely engage in, like hiking, camping, metal detecting, geocaching, and photography. Most of the time, I typically stay engrossed in online Christian interaction, like these forums and others.
Isaiah describes the new heaven and new earth as a place where you can build your own house and grow your own food. I would imagine there are limitless things to learn about God's creation, as well as a whole universe that could be explored.
Isaiah 65:21-23 And they shall build houses, and inhabit them; and they shall plant vineyards, and eat the fruit of them. They shall not build, and another inhabit; they shall not plant, and another eat: for as the days of a tree are the days of my people, and mine elect shall long enjoy the work of their hands. They shall not labour in vain, nor bring forth for trouble; for they are the seed of the blessed of the Lord, and their offspring with them.
Paul describes something so fantastical, that we can't possibly imagine it.
1 Corinthians 2:9 But as it is written, Eye hath not seen, nor ear heard, neither have entered into the heart of man, the things which God hath prepared for them that love him.
I don't think we'll be bored. As to whether we'll have games in the new heaven and new earth, I suppose we'll find out. The difference would be that there wouldn't be the sin component anymore. I envision our activities centered around God's creation for us, and not artificial worlds or constructs, as they would be distractions.