Should I return to Portugal in my months off?

I was offered a job in Tokyo. I'll be working 28 days and then I'll have 28 days off. During the working days I'll have accomodations, but during the 28days off I'll have to look for something.

Is it easy to find apartments for rent only for 1 month? Also somebody suggested me that i should rent outside of Tokyo because it might be cheaper. What cities are cheaper to rent than Tokyo and at what price?

The few prices that I've seen for 1 month rent in apartments are around 800€ (110k yen) wich is roughly the price of an airplane ticket (with return) to my country. Even if i find cheaper apartments with food costs and all normal expenses that might come, I'll always spend more than these 110k yen right?
The reason I'm asking is because I was thinking of returning to my country in some (not all) of the months that I don't work.

Finally, and sorry if this is too long, I'm scheduled in my dentist to put braces. Should I do it or cancel it? If I do it can the monthly treatment be easily transfered to a dentist in Japan? anyone had any experience with braces in Japan?

Once again sorry for the long post. I would really apreciate all of your inputs. Thanks.

That's a lot of trouble... is there a way to keep accommodations for the long-term and just ask the company to pay for it those months you are working? Or is it like company housing or something?

IF you're only wanting a place to stay for 1 month, something like a share house, backpacker's hostel, etc. will work better for you. Most apartments prefer long-term contracts, and it is a huge hassle to move in and out every month.

As for the braces, I can't help with that question, sorry.

thanks. yeah it's like company accomodations and I have to move out when I'm not working. It's kind of a hassle but it's not that bad. I can live in different parts of Japan each month.