"Sometimes there are festivals, like Japan or Korea festivals, where ..."
You have to go to
Here's one fun activity you can do
Don't forget to check out one of my favorite places
There are many shopping places that offer very cheap price, such as Tanah Abang, ITC, etc. Lately there are also many parks where the locals like to visit, since it is free, such as "Taman Menteng", "Taman Suropati", etc.
Enjoy a meal at my favorite restaurant
Kota Tua is a good place to try traditional food from Jakarta. There are many food vendors there, so you can try various food with very reasonable price. But be careful, if you have sensitive stomach. If you want a better and nicer place to eat traditional food, you can either go to Plaza Indonesia or Mall Kelapa Gading (places that I know; they have one space especially for traditional food).
Here's a doable bucket list for you to do in one day
You really need to visit "Thousand Islands". You can do water sports or just dive and enjoy the view of the sea. But choose islands further from North Jakarta. The further, the clearer and more beautiful the view is.
My extra insider tip for you is
Sometimes there are festivals, like Japan or Korea festivals, where you can enjoy the food, drink, and cultural events from Japan or Korea.