Some of the data may be on a MicroSD card, if your phone has one of these. You can read that one with a USB reader, but your contacts will most likely not be there.
With Android phones, you might be able to take another phone and log into the same Google account on that one. There's a chance that your Google account will have a partial backup of what's on the phone. You may be able to check this some other way, but I'm not that familiar with Android/Google. Best to try other options first, plugging it into a PC would be my first attempt as well.