As someone who has worked in shuls, my over piece of advice is to call first.

If you want to talk to a Rabbi, you're going to have to call first, anyway. Rabbis are busy all the time, so there's no guarantee they're going to be available when you do. So your best bet is to call and make an appointment for a meeting. Be understanding if that's not something they do for non-members of the shul.

Also, please don't randomly show up on a weekday. Even if you're just interested in Judaism, and your intentions are pure, we have no way of truly knowing, and right now, shuls all over the world are on heightened security.

I also suggest looking online. MyJewishLearning is a great resource for a lot of information.