I've been working with the Galaxy Nexus for around a week now, I have to say that is is a pretty nice piece of hardware, of course there are spots that may improve, but as it is is a really nice cellphone.
One of the first things I notice is that it is really lightweight, it weights more or less what the Nexus One does, and the size difference is huge. Of course, most of the phone is battery ;-). it has to be because of the big screen.
The phone reacts pretty nice to touch events, all applications runs smoothly and have to wait almost nothing to open them. This is in part because of the CPU power but also because of the Operating System.
I bought is with Ice Cream Sandwich, and I made the upgrade to Jelly Bean, but not over the air. Google took his time to roll out the upgrade, and Since everyone was enjoying it but me I made it the hard way, unlocking, installing the recovery and then flash with the right Jelly Bean ROM, that left me with Android 4.1, later, the OTA upgrades gave me 4.1.1.
The camera takes very nice pictures, the gallery app is nice too, reading books here is pretty pleasant thanks to the big and crisp screen, I think I'm not going to buy that tablet that I was thinking to get just to read ;-).
I'm pretty happy with the phone, I love it. I use the phone mostly to check my emails while I walk to the job, reading, checking twitter/Facebook and taking pictures. I'm not a gamer (I do play, but really easy and no graphics demanding games) so, the graphics chip is more than enough to me.
Of course, as I've already said, there are improvement spots, like the battery but this is a course that most smartphones suffer. The [soft] keyboard. I like a lot more the Gingerbread keyboard, and the power buttons in the notification area (also present in gingerbread) are missing.
So, Again, I'm pretty happy with this device, I love it, and you should give it a try.