Don’t think you’re saving money by living 30–45 minutes outside of Tokyo, because you’re going to miss so much in your life whether it’s literal time, the stress, or the aggravation of riding trains in rush hour and standing up next to sweaty people. It’s just not worth it.
Let’s say you found an apartment 30 minutes outside of Tokyo for ¥100,000 and that fits your budget. Sure, it might be more spacious, but at what mental cost? Having to commute every day plus knowing that you have to a 1–2 hour trip ahead of you if you want to hang out with friends/coworkers.
You can live in the center of Tokyo for a ¥100,000, you just have to look for it. While it’ll be a lot smaller than you might like, you probably won’t be home that much anyway. You’ll be to walk to walk/bike to work or go home after partying all night at Roppongi. If you do have to take a taxi, it’s not a $100 taxi ride, it’s a $10 taxi ride.
Final tip: Living within the Yamanote line will make your life a hundred times better. For a little bit more money or a little bit less space, however you want to look it, the money will be saved in taxi rides your first month, and the space you just got to get used to.
Here’s a pic of my first apartment in Tokyo when I was moving in. It was smack dab in the center of Shibuya and cost 126,000 yen per month (not including utilities). Roughly 32 square meters.