The White Mountains region of New Hampshire is a beautiful area with lots of things to see and / or do . Summer brings folks to the area to enjoy all the lakes and rivers as well as hiking in the White Mountains. It can get warm in the summer but it's easy to cool off. The rivers tend to run cool (temperature) and you can always pick a Mountain top to cool off. (It might be 80 degrees in the valley and in the mid 30's up on top of Mt. Washington. (Tallest east of the Mississippi)
Fall brings the foliage and the tourists come from around the world to view it here. Its still warm for hiking but might be considered a tad cold for swimming. It is such a popular time , it can be difficult to get a hotel in the area. Columbus day weekend is the basic target time but peak viewing / color can be plus or minus a week or two.
Winter brings Ice and Snow, Skiing, skating, snowboarding, Snow-mobiling (miles and miles of trails) , snow shoing, Ice climbing, Apres-skiing (also called clubing!!) and even snow tubbing ( with tubing lifts !!) are all available. North Conway Scenic Railroad also has a Polar Express that is incredibly popular with ticket lotteries , but the (pretty full) local hotels , often have ticket packages.
Spring brings the melting snows and fast rivers, the greening of the mountains and the spring rush in the National Forest. and it all boils down to Maple Syrup !! Good Stuff !!
Fly into Manchester, NH (about an hour), Boston, MA (about 2 hours) or Portland , ME (about an hour-15) all are big airports with multiple airlines and rental car companies.
ENJOY!!