I'm another who says recumbents deserve consideration here.
But before I get into that......

One bike that a lot of people get for casual riding is the Giant Revive. It has an upright position (no hand pressure) and it has a rear shock, that protects the spine from jarring bumps. The downsides I've heard of are that the bike's weight and gearing are far from ideal for anything but casual short-distance riding. A lot of "regular" bike shops are Giant dealers that have one on hand to test out, so it's worth looking at.

Back to recumbents--there is a wider variety of rider positions among recumbents than there is for upright bikes. Some recumbents sit fairly upright, while others are more reclined--and the reason this is important is that a reclined seat means that the spine isn't compressed when you ride over bumps. Also, you won't need padded shorts, and you're far less likely to get saddle pain on a recumbent.

Wizwheels makes an inexpensive tadpole trike ($1400), Sun makes some inexpensive recumbent bikes (EZ-1, $600) and delta trike (EZ-3, $800).
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If a person has a back injury, they really need to test ride bikes before buying anything. That can be a hassle with recumbents because of the lack of local dealers, but this can make the difference between having a bike she can ride, and not riding anything at all.
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