Santa's Village 10 minutes east on Route 2 (Frugal Ed, one price pays for all day all rides. Bringing picnic lunch OK) Most rides are under cover, so it's still worth going to if there's a gentle rain.
Six Gun City, 20 minutes east on Route 2. Great carriage museum too!(Frugal Ed, one price pays for all day all rides.)
Clark's Trading Post, 45 minutes south on Route 3 - Excellent! Has a great Black Bear show. These bears have really got it made. Also be sure to go in the Magical Mystery Mansion and try to figure out which end is up, take a ride on the train behind a wood burning locomotive. Look out for bandits! A great deal more there, plan on spending the day. (Frugal Ed, Very few extra costs, optional)
Hobo Railroad, 45 minutes south on Route 3
http://www.whitemtn.org/whale.html">Whale's Tale Water Park - About 45 minutes south of Lancaster on Route 3.
Storyland - 1 hour west on 302, then 1 minute north on 16
Heritage New Hampshire - (Beside Storyland)
Lost River Gorge - South of Lancaster on Route 3 and 93, then west on 112. About 45 minutes to an hour from Lancaster in Kinsman Notch. A very interesting natural gorge cut through the rocks by Lost River. Admission charged. Wooden walk with railings. Some caves.
Polar Caves - About an hour and a half south of Lancaster, Route 3 and 93 to 25 west. Another natural rock formation with caves, a zoo, more.