If she only wants to read books (and not stream video, surf the web, use apps, and play games) then an e-ink e-reader will be just fine! If apps or streaming the web or a movie sounds appealing then one of the newer tablet types would be better (
amazon Kindle, Nook color or their new tablets)
For e-ink its pretty much Amazon Kindle vs. Barnes & Noble Nook. They're pretty similar in functionality. You can get library books easily on both. The basic non touch screen Kindle is $69 which is awesome, a basic Nook would be $99 but it's a touch screen, maybe someone else will say differently but I think the only difference in the basic Kindle vs Nook is the touch screen and menu (Nook's is a little more elaborate, it shows cover art for books I believe, where as the basic Kindle is just a list of the title and author which is just fine) and price.
There is a lit Kindle and Nook and they're both $119, both are touch screen.
A not too pricey option would be the $69 Kindle, it may be a little "no frills" for some but if I needed to replace my Kindle today as much as I would LOVE the Kindle Paperwhite (the lit one) for the price difference I think i'd go with the $69 and just continue on with my book light reading at night. The $69 Kindle is wifi only so she'd have to be somewhere with a wifi connection to buy a book and get library books (sometimes you need to connect via USB to download a library book but not always), there are more expensive versions with 3G so if you were out of town without internet you could buy books but if you load up with books before you leave it shouldn't be a problem (I have yet to need the 3G and I paid extra for it) and with Amazon they have something called "special offers" which seem like ads, just FYI it does NOT show up at all when you are actually reading, its a small banner at the bottom of the home screen and as your screensaver when you aren't reading. Having the "special offers" makes the Kindle cheaper and in my opinion they aren't bothersome at all.
You didn't mention an age but the new Kindles have parental controls if that would be a plus for you, if that isn't an issue and she's older there are websites that e-mail you daily with a list of free books (they aren't best sellers but I've found a few that were really good and I've got PLENTY loaded onto my Kindle if i'm ever travelling and run out of stuff to read or something) pixleofink.com and ereadernewstoday.com but if she's young I'd suggest you using those sites and picking kids books because there are romance novels and adult books on there, also with those sites I always tell people to double check the price because while it may have been free at one time it at any time can go back to a cost so double check before you buy.