Best way to leave a job after 3 months?

I'm planning on leaving a job I've been at for 3 months. I took the job because I thought there would be a lot of hands-on and interactive work because that's what the recruiter told me but it has been nothing but updating excel sheets, powerpoints, and useless meetings. The recruiter told me during the interview that their health insurance sometimes takes a little while to start. What she meant by this is that employees are eligible for insurance on the month after their first 30 days of employment so I was out of health insurance with a wife and son for 45 days.

I told the job that I had 3 weeks of travel scheduled this month overseas and they agreed to cover the travel when I got hired (even put it in the contract) but I am planning on putting my notice in upon my return. What is the best way to go about this situation? I'm tempted to give one week notice considering the circumstances. It doesn't help that they don't pay out vacation time when you leave so I felt like I needed to at least stay through my vacation. Any help is really appreciated.