Polish your resume on the plane.
On the one hand, you may come back and land a job in two weeks and you might kick yourself for jumping right back in. However, just as possible--and it's easy to get a distorted view from sites like this--the process could take quite a few months. And, if that's the case, you might regret adding a month to the process, especially if events happen in the interim that make finding a job harder for whatever reason.
You absolutely can take some time off and work on projects, go hiking etc. For technical professionals, it's probably not that useful to make direct job hunting an 8 hr. per day task.However, there are advantages to making it a continuous process even if it's only part time. (Also, as someone else mentioned, there may be reasons to make it continuous because of unemployment benefits.)
If one is comfortable financially, I certainly wouldn't say you can't take off on a modest vacation. But it is a bit of a gamble.
...but yea, also file for unemployment immediately. Your former employer paid for that safety net.
When a potential employer inquires as to a gap in time on your CV just say you went and did some traveling and "recharged your batteries." It is completely respectable and envious thing. Also you will be glad when you are sitting at your desk at your next job working late that you went out and saw some of the world. Likewise you will also be glad when you are sitting on a beach in Southern Thailand somewhere :)
So, enjoy the time off. But keep an eye on your financials. Don't wait to start collecting unemployment benefits. Don't wait to start planning - whether that means contacting recruiters or planning a pet project - start doing something soon.