I am about to finish my Ph.D. soon. It was in the field of computational sciences and was done from a well-known European research lab. In my own assessment, it has been a mediocre Ph.D. for me (2 paper in top tier conference, 2 in average ones, no journal yet).
I am looking for post-doc as the next step. I already have a couple of offers for post-doc, and one of them is from a famous professor in my field. However, he happens to have setup his lab at a relatively unknown university in a small city in central Europe.
I was obviously aware of this while applying, and I honestly thought this wouldn't bother me at all. However, now that things have moved forward and the time has come to finalize a decision, I do find myself a bit bothered with the stature of the university. I have tried to seek advice on this matter from my current Ph.D. adviser. However, she knows my prospective post-doc supervisor in person and has been offering highly diplomatic suggestions about the matter.
So I thought it might be a good idea to ask this question over here. Please share your opinion on this. How much does the stature of the university matter in a post-doctoral position, given that the particular lab I am going to be associated with is headed by a famous name and the job description seems to suit my research interests quite well? I have other post-doc offers from relatively younger/less-famous professors from better universities. Given that the area of research is more or less similar in all the cases, what is more advisable for a career in research?