I've done all 3 (international roaming, SIM, mobile wifi router), each have their merits.
#1). On business, I just do roaming. It's the easiest... but also the most expensive at $10 a day. The absolute biggest advantage of this is being able to make phone calls without using VOIP.
#2.) For personal, solo travelers are best served by SIM card rental, especially if you have a newish unlocked phone. For non-technical people, installation can be confusing... although there are hundreds of websites that detail the process, should be easy enough at this stage in the game. Once you clear customs at Haneda or Narita you can find kiosks selling SIMs, I used the brand "b-mobile" and it cost me around $50 for 15 days with a 3GB/72hr (rolling) capping out at 10GB. I never hit either cap but if you do on the rolling, you get throttled to 200kbps until the 72 hrs period is up. If you hit the max cap, you can pay to refill your card, it's something like $10 for every additional 5GB. I'm not a big data user though, and if you keep it mellow with the streaming & video watching/uploading until you're back on hotel wifi, it's highly doubtful you'd hit that. It should work out to be around $3-5/day depending on the plan you choose.
#3.) For couples/groups (esp. ones that will be sticking together), renting mobile wifi routers are great. It's a little more expensive than SIMs but because you can port in up to 8 devices, it can be a great cost savings, even with 2 people. The only disadvantage to the mobile routers is they are battery hogs (they usually come with back up battery packs) and all that gear can add up to more crap (cases, cords, backup batteries) one person needs to lug around & then remember to charge up every night. Also if you need to split up, the person not carrying the router will be left to their own... uh, devices (lol). The data plans work on the same network as the SIM cards (see above). As long as you arrive at an hour when the airport post office is open, your rental agency can arrange to pick up once you clear customs, or have it sent to your hotel/airbnb. 15 days capped out at 3GB/72hr (rolling) was $75 split between 2 people worked out to be ~$1.50 per person per day.
I spent a lot of time in Japan pre-mobile web and the advances in tech (google maps, google translate, hyperdia) have made tourism incredibly easier in this day & age, which explains there is a massive tourism boom. The amount of resources available on travel sites is extremely helpful as well.