You should check what software its running (ie. Android, Windows mobile, etc.) A quick Google search shows the LG Quantum runs Windows Phone 7, which B&N has not come out with an app for yet. If you want a phone that already has an app that will run, you should get one running Android, a Blackberry, or an iPhone. There is a "beta" app written for the HD2 which can run on any other Windows Mobile 6.5 phone, but you have to do some hunting to find the download.
If you want a phone that already has an app that will run, you should get one running Android, a Blackberry, or an iPhone.
To build on KingAl's response, you probably don't want a Blackberry, either.
The reader app for Blackberry is the Reader app, not a NOOK app. It does not work with all books one purchases and reads from B&N (reportedly) and it doesn't reliably sync back to NOOK, either.
I've only used it once or twice, so the above is hearsay, but I wouldn't repeat it were it not from sources I trust, at least a little.
It looks like you want an Android phone of some sort. Several users here have great luck with their Droid X phones. I'm currently considering a Samsung Fascinate and while I know the NOOK app exists, I can't find any reviews from someone actually using it. I doubt I'll ever read much on my phone, but I suppose I do want to know that I could...
As long as you're considering a smartphone, you might as well go for the Motorola Atrix. It's the best Android phone out there at the moment, and it's surprisingly reasonably priced ($149 on contract).
It is a sad situation that B&N ignores WP7 and RIM/BB platforms to release a nook app. The BB Torch and all WP7 phones have been available for almost 6 months, and still no nook app. If the nook app does disappear from iTunes, where does that leave B&N? With a bunch of customers checking out the Amazon Kindle app, that's where.
xmier, if you are updating a current phone, you owe it to yourself to visit Amazon Wireless. They have all the smart phones and deal with all the carriers.
I recently updated to a Samsung Captivate and was able to do everything from the Amazon web site. Best of all the phone cost .01 and free 2 day shipping.
Doesn't get any better than that!!!! BTW, the Captivate has been updated to Froyo 2.2....