It is important that you visit the lab and get comfortable with the environment before you accept any offer. I made a mistake accepting an offer before visiting the lab or deep investigation on the research quality, and now I am thinking to quit.
You can simply say that you are interested in the PhD, and many professors will ask for a meeting or interview, then you can propose a visit (if he doesn't ask for it).

Good luck

It is funded position, and the replacement PhD will be also funded, but in Europe PhD students are hired by the university as researcher, so it is like quit a normal job. But I am thinking to quit soon because I don't want to "take" so much money from the project funds then leave, and to allow them find someone soon. If I continue longer time it might create problem for the project if I leave.

You may have a point on the fact that supervisors might not look kindly on me, so I will not quit before I find another opportunity, hopefully soon.

Hi everyone,
I would like to share my experience with you and ask for advise and suggestions. I graduated with a Msc with honor from a leading university in my field (top 10). Afterwards I accepted a phd offer in an interesting project but in a small university. Based on some suggestions, I have been told that it is a good place and good working environment. But in the first month I realized that the atmosphere is not stimulating, original high quality research is not conducted and facilities are not as I expected. So I am thinking to quit now given that I spent only one month here, and find another PhD opportunity somewhere else (I strongly want to do a PhD).

Probably it was a mistake to accept such offer without deep investigation on the place, but it is better to correct a mistake early rather than continue and regret afterwards.

What do you think about this situation? I appreciate to hear from you.