I have solved this exact requirement by purchasing an HP Photosmart 6520 wireless printer. Works like a charm.
I have an iPad with 4G cellular, and I have no wireless router for Internet in the house. My only Internet connection is 4G through Verizon cellular. I have no wifi router, hence no wifi network.
The HP 6520 has a "Wireless Direct" mode, and the setup guide tells you exactly how to set it up for wireless printer if you have no wireless router.
You set up the wireless direct through the touchscreen menu, and the printer publishes its own SSID.
On the iPad, and also my iPhone, I connect to that wifi SSID.
Then using the iOS print apps in Mail, Safari, Photos, etc. - Print to the HP Photosmart and it works perfectly.
No router needed at all.
And the cool part, I can print Photos from the iPad or iPhone to the Photosmart, which has a nice 4x6 photo paper tray, and the Apps and printer are smart enough to send it directly to the photo paper (vs. the normal 8x11 paper).
And this particular printer will print 2-sided if you want it to, and this option is presented to you in the iPad and iPhone printer dialogue.
This printer was $110 at Best Buy. I am quite a happy camper. Getting one now for my mother also who has iPad with 4G but no wireless router.