Unless you really like cruisers and their riders, the last week you want to go is Bike Week.
During the week, all the roads will be crowded with cruiser riders and often groups. This can be incredibly frustrating. Add in that every roadside place will be packed for lunch, dinner, and even breakfast. The 'magus? Parade ground - last time I rode it during that time of year, I did it East-to-West at 6:30am on a Monday.
The population of the state of New Hampshire is about 1.3 million. During bike week, 250,000 to 350,000 bikers visit. Most of the hotels, campgrounds etc are filled to capacity. Every cop in the state is on duty. A lot of the people are older, professional, and perfectly nice. But there are bad pennies in every jar.
Going the week prior isn't bad, though everyplace is starting to get crowded.
2005 DL650 (sold) | 2009 DL650A (sold) | 2008 Tiger 1050 ABS | 2012 WR250R | 2008 CRF100F