Some regions around Frankfurt are famous for their wines. When I was in Frankfurt last time, I tried their Apple wine and simply loved it. This time, I will be in Frankfurt for a longer period and would like to try some more of their famous wines. I have not tried any special wines before and most probably will not spend a lot on wines. So please suggest something for a beginner within budget that is available in Frankfurt main city area.
I would spend your limited time and money just tasting wines from one region. Nahe is a smaller wine region just west of Frankfurt, and I've found the wines there to be good quality, with individual charm (in other words, without the sense that they are mass-produced). More info here
By all means, talk to locals: the people you're visiting, the clerk in your hotel. That's almost always a great way to discover something.