Osaka - Tokio Hokuriku Arch Pass + Metro in Tokio

Flower

Hi,
Im planning on visiting Japan for 12 days, of which the first 4 days in Tokio, and the other 8 traveling towards Osaka. The plan is to visit Kanazawa and Kyoto along the way to Osaka. The full JR pass for 7 days is more expensive than a 7 days regional Osaka - Tokio - Hokuriku Arch Pass. Is it worth it to only buy the regional pass for 7 days, and for the metro/busses in Tokio just separate tickets (or any other alternative for public transport in Tokio) ? Or is it easier and cheaper to buy the 14 day JR Pass, as it makes traveling by public transport in Tokio possible?

Tenjin

If you don't travel enough, you will lose money on a rail pass. The Hokuriku Arch Pass is a good choice if you are also going to see Kanazawa & Kansai and return within 7 days. Be sure to see the Kenrokuen Garden in Kanazawa - it is widely regarded as the finest in Japan.
https://goo.gl/MkGZYp
You probably don't need any buses in Tokyo at all - you might end up in a traffic jam. So if going all over, a 72-hour subway pass can give some good savings.
https://is.gd/WoFeIw
Or, you can use an IC card like Suica or Pasmo (the latter has no refund charge if you refund the balance). There's little savings in them, but there are very convenient.
https://www.japan-guide.com/e/e2359_003.html

Flower

Im planning to end the trip in Osaka, from there on out I take a plane, is it necessary to return to Tokio?

Tenjin

No, not at all. It can save you several hours returning to Tokyo if you can fly out of Osaka. Although some airline fares might be different doing that, so in the end you have to consider the costs of everything. If you just go one way though, then you probably will do better with no rail pass at all.

Flower

No rail pass at all? What do you suggest then if I want to travel from Tokio to Osaka, whilst visiting Kanazawa and Kyoto?

Tenjin

If you are going just one way, and flying from KIX as you mentioned, then I don't recommend any pass. You'll save more just buying regular tickets.
You could save a little with the Icoca & Haruka discount ticket
https://www.japan-guide.com/e/e2359_icoca_haruka.html
unless you get another IC card like Pasmo or Suica in Tokyo.