If you want a lot of action, shops, restaurants, and busy traffic and such I'd say North Conway-Conway strip would be your bet.
If you want a quieter town feel but still with stuff to do .
I'd say check out Franconia
North Woodstock is also a charming village with things like Clark's Trading post and Franconia Notch State park nearby. with the Cannon Mountain Aerial Tramway...(great view)
Definitely take the car up Mt washington as well
and take the gondola up Wildcat Mountain and hike part of the AT(Appalachian trail)
The lincoln -Woodstock/No.Woodstock area would be great for you
has lots to do - and is close to everything int he White mountains and Vermont as well
This Week in Lincoln Woodstock - Lincoln Woodstock NH Chamber of Commerce
Clark's Trading post in North Woodstock is a must stop
Clark's Trading Post - Trained Bears, White Mountain Central Railroad, Antique Museums and the best in family entertainment
Check out the bear show! and browse the cool store.
You must also check out the Flume Gorge natural area
in Lincoln
The New Hampshire Division of Parks and Recreation
Hobo Hills Adventure Golf
is in Lincoln and North Conway
Pirate's Cove Mini Golf, Putt Putt Golf, Adventure Golf, Miniature Golf
The Hobo RR is in Lincoln NH
Scenic Railroad Train Rides on the Hobo Railroad and also the Winnipesaukee Scenic Railroad in New Hampshire
Loon Mountain resort has hiking trails a skyride to the summit
Summer Vacation & Winter*Ski Resort*Destination in the New Hampshire*White Mountains- Loon Mountain
Lost river gorge and waterfalls in No Woodstock
Lost River Gorge & Boulder Caves | Get Ready for an Adventure!
Mt Washington Cog Railway
Mount Washington Cog Railway
Bretton Woods NH
Lincoln NH also has the Whale's Tail Water Park
Whales Tale Waterpark
White mountain motorsports park
No Woodstock
White Mountain Motorsports Park
While in the North Woodstock, Franconia, Lincoln area you should def. have breakfast at Polly's Pancake Parolor well known for breakfasts!
and well, pancakes in Sugar Hill NH
Polly's Pancake Parlor - Sugar Hill, New Hampshire
Other attractions include:
Santas Village - Jefferson NH
Santa's Village :: Jefferson, New Hampshire
Story Land - Glen NH
Story Land
Flossie's General Store - Jackson NH
Jackson New Hampshire Chamber of Commerce
The Covered bridge in Jackson Nh
Another good home base might be Jackson Village NH
at the
Lodging, Mt. Washington Valley, NH, White Mountains
Covered bridge motor lodge
Mt Washington Auto Road
Mount Washington Auto Road
Conway Scenic Railroad
Conway Scenic Railroad
Dan's Scenic Moose Tours
http://www.dansscenictours.com/
Pemi Valley Moose Excursians - Safaris
Lincoln NH
Pemi Valley Excursions, L.L.C. Moose Tours
SO to sum it up I'd say you have four options
Lincoln/Woodstock area would be your best bet or Franconia
followed by
Jackson Village
then Gorham
and finally Conway/No. Conway area