Do you have hilly terrain? If not, a single speed could be an option. Generally, a CX bike or a "sport-touring" bike might fit the bill. Less aggressive than a full-on road bike, with rack mounts, etc. and the capacity for 28-35mm tires that offer more comfort and stability than the 23-25c tires on most racing-oriented road bikes.

Have her test ride some LBS bikes of various styles to see what she feels the most comfortable on. Check out local sales - who knows, perhaps there is a great deal out there.
Craigslist is good if you really know what you are after (size, style, quality), but is a real crap shoot if you are unsure.
BikesDirect is a great way to save some money, but their lower priced bikes typically have horrible saddles, so plan to spend $50-100 for a good quality female-specific saddle (Terry, Specialized BodyGeometry, etc), which will make a tremendous difference in her enjoyment of the bike.

I'd recommend against a racing bike (short wheelbase, steep geometry, aggressive rider position), at least initially, as they tend to be less comfortable and stable for new folks.

This would be a nice start. http://www.bikesdirect.com/products/dawes/ltcross_x.htm