You mentioned her interest in fitness. You can point out that cycling is a great exercise: it's easy to hit the sweet spot between walking and running, and it's low impact on the joints. Plus it's a great way to get to know where you live.

But you've got to start with her goals and interests. It's no crime to not be passionate about cycling: you can be interested in it without making it the focus of your life. If she tries and decides that it's not for her, that's her prerogative.

If the bike she has is what she can afford, then focus on fixing it up: lube it, adjust the shifting, and replace anything that is clearly dangerous. If her college has a bike co-op, she can go there for a better (used) bike if she decides that riding is something that she wants to continue.

I don't know whether plantar fasciitis is a problem for cycling; I had a mild bout during my running days but fortunately it passed. I did develop recurring knee problems when running, which is one reason I got into cycling. You should make sure her saddle is high enough (knees just slightly bent at the longest extension, or fully extended when the heel is on the low pedal) and encourage her to spin quickly in a low gear (I aim for 80-90 rpm) instead of using too high a gear and stressing the knee.

AndrewP's advice on learning to ride is good: take off the pedals, lower the saddle, and focus on coasting downhill, balancing, and braking. Once she's mastered that, replace the pedals, raise the seat to the proper height, and she should be good to go.