Being a NEET isn't so bad for the first few weeks. After that it can easily become a hellish nightmare existence where you're essentially a living corpse. You don't want that.
The problem with being a NEET is that you have a lot of free time, but no direction on how to spend it. This often means regressing into a routine of waking up, browsing the internet, and going to sleep unfulfilled.
While I'm no expert, I do have two very simple pieces of advice that have helped make my life less boring, at least a little.
They're by no means a silver bullet, and you'll probably still have bad days, but it's marginally better than every day being a bad day.
Get a Website Blocker
Installing a website blocker is relatively easy way to get out of the habit of wasting days browsing the same websites. I've found that even a simple, easy to circumvent one can help, as half the time you end up on these sites out of habit. You just need to remember to turn it on.
There are many you can choose from, but Leechblock is probably fine for most purposes and you can install it as a browser extension.
Pick up Some Hobbies
As a NEET you have a lot of free time, so you may as well pick up some hobbies you otherwise wouldn't be able to. There are many benefits to this, but the most important is that you're giving yourself work to do, which will stop you going crazy. You'll also learn some new skills along the way, and some of those might even help you leave NEETdom.
It's very easy to just say "get a hobby", but that's pretty useless advice, and I don't want to give useless advice.
Some people want to know how to get started with hobbies; for me it was a case of seeing something someone else was doing, and thinking "it would be cool if I could do that", then taking steps to get there. That's still quite vague, so below are the hobbies I picked up and how to get started with them. Most can be done in the comfort of your own home.
Learning the Piano
You need to have a piano in the house to start this one, so it's probably the least accessable of the hobbies here. It also helps (but isn't necessary) to have a teacher, and unless you live with one, it's going to be very, very expensive.
If you're undeterred by that, Jibbidy F and A C E is a very good starting place. As an adult you'll fly through it, but it's very important that you start simple and don't overwhelm yourself. After that you can move on to John W. Schaum's Piano Course A and then B. That should last you about a year with a few minutes of daily practice.
You can, of course, learn another instrument, or music theory which doesn't require one (but it would help).
Learning Japanese
As you've probably guessed, I consume a lot of Japanese media, but what made me pick the language was finding out professors get paid about twice as much as they do where I live and there's somewhat of a push to hire foreign academics at the moment. Knowing Japanese would also help for IP law, as it's a fair bit more protective than in the west, which would make for some interesting analysis. Plus the cartoons are pretty good, I guess.
As for learning the language, if you are reading this you can start right now. itazuraneko.neocities.org is was a very comprehensive guide (now mirrored here) that only requires a few years of your time. If you work on it daily, you will see gradual progress.
There's plenty of other (more useful) languages out there, with plenty of resources, so just pick the one you like most.
僕の日本語は下手です
Learning to Draw
Admittedly, this one is by far the least enjoyable and most time consuming hobby I've picked up. Progress is painfully slow as well and you just feel a bit rubbish by the end, so I'd only recommend this is you really, truly want to draw.
I also probably shouldn't tell you how to draw, because I'm not very good at it. Books by Andrew Loomis get recommended a lot. I also found this video to be quite useful, but I cannot comment on its effectiveness.
Learning to run
Couch to 5K is a good starting point.
Running shoes and a track suit are optional, but advisable.
Learning Origami
Origami is very easy to get into, you just have to buy some square paper. You can find instructions for models very easily and it doesn't take too long before you can start doing quite complicated models. It does reuire a fair bit of patience, though, especially if instructions are unclear (which is more often than you'd like).
I have spent many evenings folding paper while watching Futurama. I'd recommend it.