Train ticket

If I am in Tokyo for 4 days, going to Disneyland, Hakone, and shopping around Shibuya and Harajuku, Shinjuku. Is it worth buying an Japan Rail Pass? If not, is it just buy the ticket when I need it? Where to get in Singapore?

Jessica

You need no JR Rail Pass, this is only for long distance travel. All but Hakone is within Tokyo and a Yen 160 to Yen 300 ride, For Hakone think about the Hakone Free Pass what includes the train from Tokyo Shinjuku railwaystation. See under Hakone here in this guide. Tickets you cannot buy in Singapore but immediately prior to your travel, similar like buying a subway ticket for Singapore subway. Similar stored value tickets are available, too.

as peter said, you don't need a JR pass.
You can check out Japan-guide's guide on the Hakone Free Pass here http://www.japan-guide.com/e/e2358_008.html

What peter is mentioning, Tokyo has the Suica which is very similar to the Ez-link card in singapore.

When you 1st purchase it (from the midori mado guchi offices in most JR stations), you'll pay 500yen deposit + 1500yen card value.

I think that should be sufficient for your 4 days trip in tokyo. if you have any remainder value you can refund it back (but there will be a small tax value)