Head to the village of Jackson for bridges and falls.
There are a lot of covered bridges in NH, all over the state, and many waterfalls in the White Mountains. The NH Bureau of Tourism website has a lot of information about them and where they are www.visitnh.gov. Look under <What To Do> in the drop down menus. There is a link for <Lakes, Beaches and Water Fun> that will have a link to Waterfalls. There is also a link for <Covered Bridges> Follow each of these links and you will have a ton of info.
As for the waterfalls, do you want to look or get in them? Some are easily reachable by car and an easy walk, while others require some hiking commitment. Diana's Baths is popular and easy to reach,a nice place to get int he water. It is reachable form West Side Drive in the N. Conway area.
There is also a nice falls the comes down behind The Basin in Francoina Notch. Follow the signs for the Kinsman Mt Trail, and it will lead you to a falls that cascades about 1/2 or more down the mountain. Immediately accessible, but you can hike up as far as you want.
To see both in one stop, would agree with Red Rox that Jackson is the place to go -- a nice, small village just north of North Conway on Rt 16 -- if you come in from the south (from Glen), you'll drive through the covered bridge as you come into the village. Continue through the built-up area to a small, arched bridge....then take an immediate right up the hill and watch for the parking area on your right..... Series of several falls and ripples (depending on water volume) immediately on the roadside...
We like to stop at the bakery/deli beside the Post Office in the village and grab a lunch-to-go, then take it up to the falls and sit at one of the picnic tables there...enjoying the water while we eat....
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