I'm working on a web based ladder system for a game. It is very game specific and I want to make the project open source so the community can give back, contribute and make the experience better for everyone. However at the same time I don't want people to re-use the code/implement the code on separate sites because the purpose of the website/project is to unify the community under one roof. So my question is: what is the best license to use to make that possible?
... I don't want people to re-use the code/implement the code on separate sites ...
This really misses the point of Free Software, or as the FSF puts it, it's open source but not really Free Software. Despite my tone, I'm not here to lecture you, I'm simply pointing out that people are not likely to help if the project has this kind of restriction.
However, if you change that to:
... I don't want people to re-use the code/implement the code on separate sites without contributing any modifications they make back to the project ...
Then the GNU Affero General Public License might be appropriate; it prevents people from modifying your website unless they publish their changes under the same license.
If you still insist on your original restriction, then no open source license will help you, since most of them are about being Free Software, not just open source. You're going to have to write your own license, or modify an existing one.