Best answer: If you want to use headphones for private watching, the Roku Ultra is going to be the best streaming box for you.
Amazon: Roku Ultra ($89)
Why this is the streaming box for you
Roku has offered 3.5mm headphone jacks on its streaming sticks and boxes for years, and it's still present on the latest Roku Ultra. If you've ever used another Roku streaming device — or a TV with Roku built-in — you'll immediately be at home with this remote. If not, it's super easy to learn how to use the remote and navigate the interface, and the 3.5mm headphone jack is easy to find on the side of the remote. There are earbuds included to get you started, but feel free to swap these out for your favorite headphones.
Almost every streaming service and digital store is available on Rokus, although iTunes isn't available, unfortunately. And if you're using this with a newer TV, know that it supports UHD and HDR playback.
The least expensive box with a headphone jack.
The Roku Ultra offers an easy-to-use remote and interface, and most importantly the remote has a 3.5mm audio jack for your headphones. Roku has all your favorite streaming services, and it'll work perfectly with your new 4K TV.
Why you may consider some upgrades
The Roku is great if you just need something for streaming services like Netflix, Hulu or Amazon Prime Video. But if you also want a box for games or playing DVDs and Blu Rays, it's worth spending a bit more money.
An upgrade pick
NVIDIA Shield TV
Great games and most streaming services
NVIDIA's Shield TV features a headphone jack on the game controller, so you can use that and your favorite headphones for private movie-watching. The Shield runs Android TV, so your favorite streaming services are present. Plus, it supports 4K HDR playback, perfect for your new TV.
Another upgrade pick
Xbox One S
When you want a console for your streaming
The Xbox One S controller has an audio jack for watching Netflix while your partner is sleeping. The Xbox One S features all major streaming services and supports 4K HDR playback, including playing back UHD Blu Rays.
A Sony upgrade
If you're looking somewhere else
Just like the Xbox One, the PS4's controller offers a 3.5mm audio jack for watching your favorite shows on Hulu without keeping anyone else up. The PS4 offers nearly every streaming service, as well as some compelling exclusive games.