Best, biggest and longest running fairs are 3 individual traits-pick any 2
Fairs in NH are long long-running by any stretch. My favorite is Deerfield Fair, the oldest fair in the USA, which runs a mere 4 days. It's primarily an agricultural fair, and has more horse shows than any other fair except possibly Topsfield (down in Massachusetts)
Hopkinton Fair is great fun as well, but with a completely different feel. It's an 'eaters fair' LOL with every baked, fried and sugary treat you could imagine. Big HUGE donuts, baked apple crisp, maple sugar cotton candy, lots of rides and a couple of stages (the kids loved the hypotist last year) and on Saturday night, the roar and dust of the demolition derby.
I know you asked specifically about New Hampshire's fairs, but New England's biggest and longest running fair is, I believe, "The Big E" (The Eastern States Exposition). It's HUGE, and coming all the way from SoCal, something you might enjoy seeing. Actually, I don't think 1 day is enough to see EVERYTHING at that fair, but check the website:
The Big E