What cheek you may be thinking, what makes me think I am qualified to answer this question? Some days I have to agree with you - on dark and grey days it is hard to remember I have written poems and had them published for payment.
But I have had poems published, not once, but far more often than that. Even so, I would never presume to say - "This is the only way to write a poem!"
I know different people write fantastic poems in ways that differ widely. Some must do their first draft on paper, with a particular pen. Others say they can only write creatively on their computer. Personally, I have done both, successfully or not, many times.
Some people can only write poetry if they are in a particular room, some must be at a particular place, while others seem to be able to write well no matter where they are or what sort of disaster is going on around them.
If you only write at a certain place, and won't try anywhere else, to you have a good reason for that? Have you tried to write somewhere else and failed? If that is the case, it is still worthwhile trying other times and places. It may be the time you failed just wouldn't have worked no matter what, and if you refuse to try somewhere else, you are making life hard for yourself.
Give somewhere else a go, but make sure it is a pleasant place, so that even if the writing doesn't work it's not a complete loss. I have had fun writing at my local hotel, with amazingly good and terrible awful results. It doesn't matter, I had fun no matter what!
Different poems can sometimes call for different methods. If you always write your pithy short poems on modern life sitting at your dining table at night, maybe you could explore something different, somewhere else. Perhaps give haiku a go, sitting at a public park.
It is worth a try, anything and everything is worth a try, if writing poetry is your thing.
The best place is to write a poem is the place that works for you now, which may be quite different from what and where works next time.