I feel like I want to leave without a 30-day notice.
Why do you want to do this? Any particular reason?
I have an appointment in the city
I can see that you have another opportunity, but it is wrong to leave your employer without notice, as it might impact their business. You should give at least two weeks notice, otherwise they will not give you a good reference, which you might need in the future.
I don't mind if I don't leave with a positive reference.
You don't care, but it is considered rude and you probably won't get the new job in the city if they know you're willing to quit without leaving a notice. It is considered extremely tacky and rude to just leave a job and every job after them will assume you may do the same.