Avoid the evil integers!
Python, no string manipulation

def f(n):
    n += 1
    p = 1
    m = n
    while m:
        if m % 1000 == 666:
            n += p - n % p
        p *= 10
        m /= 10
    return n


Works by finding powers of 10, p, where 666 appears, and adding p - n % p to n which replaces 666xxxxx with 66700000.