Unless you have or hire a chauffeur, and you're into photography, forget driving a private car. There are pull-offs, but the entire trip is scenic. The Mount Washington cog railway or the auto-road tour van are far better options.

https://mt-washington.com/guided-tours/2-hour-tour/

And be sure to check the weather, it's often foggy in the extreme.

Also the Kancamagus Highway is most famous for fall foliage, but offers plenty of great photo opportunities in the other seasons -- including a covered bridge and four waterfalls.

https://kancamagushighway.com/

https://nhtourguide.com/wp/places/category/waterfalls-in-nh/

There is one White Mountains photo guide I'm aware of, but it's oriented towards the fall leaf season.

https://www.amazon.com/Autumn-Hampshires-White-Mountains-Photographers-ebook/dp/B079WMVL3F/ref=sr_1_2?ie=UTF8&qid=1532369387&sr=8-2&keywords=rebecca+metschke

Just got back from NH. If you're interested in lupines, you might still get some shots. I would check the Harman's Cheese and Country Store website. They usually have some up to date photos of lupine conditions in Sugar Hill. If you go there, Sunset Hill is a great location for, you guessed it, sunset shots. There is a great view of the Presidential Range. On Kancamagus Highway, there are a couple nice waterfalls, Sabbaday and Rocky Gorge. Also there are some nice views along the highway, though at this time of year you will need some great weather conditions for decent shots.
There are some great waterfalls around Pinkham Notch. Crystal Cascade and Glen Ellis are nice.
Someone mentioned Flume Gorge. I would skip that if you're interested in serious photography. Too many people and the boardwalk is very narrow it's quite possible to upset people waiting to get by. It's been 20 years since I've been there. I don't even know if they allow tripods.
Drive through Franconia Notch. The view along the highway beside Cannon Mountain is gorgeous. And there is a nice location there called The Basin. Lots of photos there.
I don't wanna hog your thread with pictures so I will try to send some via PM.

I had a second home in Bartlett several years ago and the photo ops are everywhere. Don’t forget
Diana’s bath right off trhe main road and go to Jackson just a few miles away where the river comes right into town and the water falls are all over the place. Finally, drive out toward the Wildcat Sky area and have the river on your left all the way with several great photo opportunities. Of course, the negative is trhat this is one of the most popular areas in New England and the crowds will be great so you will havre to deal with people all around blocking your shots. Good luck, have fun.