Rankings aside, how do you guys assess the quality/strength of a certain department in your field of interest ? In particular, how do you compare the strengths of 2 departments in a certain field ?

To make my question more concrete, I am trying to optimize the potential of doing quality research work and the prospect of a career afterwards. So for example, the amount of funding, the beauty of the place and other such factors don't really count towards my question.

I face the particular difficulty of lack of an advisor familiar with schools in the US and lack of advanced knowledge in my field of interest (obviously), so I can't directly infer quality by looking at publications. Also, in other disciplines, one can look at things like impact factor of the faculty and the journals they publish in, but this approach falls short in Math since many people publish preprints. I try also to look at faculty awards, where their collaborators work, invitations to international congress of mathematicians, AMS fellows nominations, etc. If there is a more straightforward way, I don't want to reinvent the wheel.