Last year I spent 2 months right outside Tokyo (on the Keio-Inokashira line) and this year I'm here for 4 mo right smack dab in the middle of it.
Since I'm only here on a tourist entry visa, I can't get "real" services so I'm paying 140,000 yen/mo in rent (for an admittedly pretty decent place, and no "key money" and they charge it right to my credit card) and $250/mo for an unlimited data SIM card rental (can't even get prepaid without a proper visa…), but aside from those inflated costs, everything here is the same or cheaper than in Sweden. Especially eating out. E.g. back home you can't get any prepared meal aside from sloppy tax-evasion kebab for less than 90 SEK (US$13) but here you can get away with it for at least half of that.
Public transport is about the same price as at home, but it's really easy to underestimate how big Tokyo or even the whole country is. Thinking "oh I'll go to yokohama for that party" it's really easy to forget that at home that'd be the equivalent of taking the train to the next country over.
I absolutely love it though, anyone even remotely considering coming here should definitely do it, even if just for a short while. It's an amazing place.
Edit: oh yeah, I got an ear infection while here and had to go to an ear doctor without any insurance. For the first visit (which included a signup fee, a hearing test and a prescription), I paid $150, and the 2 followups each cost closer to $40 each. This sounds about right for what I'd pay at home if I wasn't european and got free healthcare (my reference for the cost of European care comes from my parents, they moved to Australia and lost european coverage so when my mom fractured her jaw when she was here for a visit she had to pay out of pocket).