Samsung Galaxy Note 5
It's starting to show some signs of age, but the Galaxy Note 5 is still one of the best big smartphones available right now. A "phablet" from the company who pioneered the big screen idea.
After the Galaxy Note 7 was announced in August of 2016 and recalled a month later, this is their only big-screen phone left. Well, the only one we'd recommend. Personally the Galaxy S7 Edge would be a better choice (with a 5.5-inch screen) but if you absolutely want the bigger screen and stylus the Note 5 is your only option.
By now most buyers should know what to expect from the Galaxy Note 5. It has a beautiful 5.7-inch Quad-HD AMOLED display, a fast processor, 32GB of storage, 3GB of RAM, no micro-SD slot and a pretty great camera. It's basically the Galaxy Note 7 with a few features missing or toned down, but still a good phone. Android 6.0 Marshmallow made it even better, and the experience should once again improve whenever it gets Android Nougat.
We're not sure you'll be able to find one unless you pick it up used, but it's an idea. Oh, and it won't explode, and you can take it on an airplane. So there's that.