Looking at a list of the top 200 grossing movies from 2006,
https://www.boxofficemojo.com/yearly/chart/?yr=2006, the only ones I've actually seen were:
Pirates of the Caribbean: Dead Man's Chest
Night at the Museum
Cars
X-Men: The Last Stand
The Da Vinci Code
Superman Returns
Casino Royale
The Pursuit of Happyness
The Devil Wears Prada
Nacho Libre
Monster House
V for Vendetta
The Prestige
Nanny McPhee
The Illusionist
Pan's Labyrinth
Akeelah and the Bee
For Your Consideration
Of that list my Best Picture nominees would have to be (in no particular order):
1. Night at the Museum
2. The Pursuit of Happyness
3. The Prestige
4. Akeelah and the Bee
5. The Illusionist (I think; it's been so long I don't exactly remember it... but I think I was impressed at the time)