You haven't said what your budget is... "really nice bike" could mean a lot of things depending on people's experience. Your new to biking so perhaps you think that $300 would produce a really nice bike...?
A Bike Friday is a really nice bike and one of their models would be very good for you but might be outside what you are willing to pay at this stage. That's only normal, beginners are willing to pay far less for a bike than experienced riders, that's also how I thought when I started out.
So going by experience, maybe a Downtube, but a BF (Bike Friday) is going to be your best bet overall, since you would keep it, whereas a low end bike such as a Downtube has limited appeal. That's not to say Downtubes are no good, in fact they offer excellent bang for buck.
I am suggesting a Downtube and not a Dahon as Dahons have sloping forward steering risers and may actually be too big. But I most strongly suggest a BF since they are built to your required size, the only folding bike manufacturer who do so.