Please be aware that if you do (1) and also do (3) you may be committing Unemployment Insurance Fraud. Most states require you to not only be actively searching for work, but to be "Able and Available" to work and frequently investigations and audits turn up fraudulent UI claims on this basis. Even though much of job searching is online and can be done anywhere, the assumption is that if you are out of state, you weren't available to work in your home state that week.
I did this. I highly recommend using the time to take a vacation. And by vacation, I mean searching for jobs in other states and countries.
I disagree with your interpretation of "able to available".
Even nolo is not 100% on this: Vacations and travel MAY mean you are "unavailable" to work.
I am not a lawyer, and this is only my non-lawyer non official, non-professional opinion of what I relied on for myself.
1) Jobs are available all over the country and all over the world.
2) If you are actively applying and interviewing and able and willing to take the next flight home in the event of an offer or unwillingness by a company to interview you over Skype.
So for me, I had a justification. If the state did not agree with me, I risked them taking the money back. I didn't exactly push it by mailing my claims in postmarked from a foreign country either. I found a way to get them mailed in from my home area as to not cause undue focus on me.
You can always just ask the employment office about out of state trips and work requirements. That assumption that you will be viewed as unable to work might not be valid. Like you said you can apply online, and you can always visit a place you are interested in working and then you will be available for in person interviews.
Source: http://www.nolo.com/legal-encyclopedia/collecting-unemployme...