Franconia notch state park has full hookups.
It's officially Canon State park on the amenities chart below.
https://www.nhstateparks.org/uploads/pdf/campgroundsAmenities.pdf
Near Mount Washington is a pretty big area...for example, Berlin is near Mt. Wash, but 45 minutes from North Conway...which is arguably the most tourist-oriented area in northern NH. There are two sides to Mt. Washington that offer non-hiking access to the summit. The Cog Railway is on the western slope and is in Bretton Woods, and the Mt. Washington auto road is on the Pinkham notch side (Eastern slopes).
If you want people and outlets, North Conway is your place.
The Franconia notch park will offer a much more natural environment in the midst of many major hiking trails and fairly close to the Cog railway. Most NH state parks do not have full hookups.
Feel free to pm me if you have any questions.
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