According to the episode The Lost Treasure of Griffonstone, the Griffons used to rule a mightly kingdom from the capital of Griffonstone.

The Griffon Kingdom had fourteen ruling monarchs from King Grover to King Guto. The Griffon Kingdom was ended when the monster Arimaspi tossed the Idol of Boreas into the Abysmal Abyss.

In the thousand-year period when Princess Luna was exiled to the moon and Princess Celestia ruled alone, I speculate that this was the era when the Griffon Kingdom ruled, including cities that once were part of Equestria including Manehattan, Trottingham, Fillydelphia, and Baltimare. In other words, a large number of ponies lived under griffon rule for several centuries.

I assume the Griffon Kingdom was often at war with Equestria, and Celestia's royal guards fought many battles with griffon soldiers.

The downfall of the Griffon Kingdom I speculate occurred about a century or two (100 to 200 years) before the time of My Little Pony Friendship is Magic.

A lasting legacy of the Griffon Kingdom was probably the fact that a relatively large number of griffons lived within Equestrian borders once the downfall of the Griffon Kingdom caused the pony kingdom ruled from Canterlot to reassert it's authority over traditional pony territories.

The fact that griffons can fly and most ponies (except Alicorns and pegasi) could not probably contributed to griffon rule over a fairly large pony population for several centuries.

The pony populations I assume were probably treated equally with their griffon compatriots under the rule of the Griffon Kingdom since the griffon kings were probably fair and open-minded.

The Griffon monarchs sincerely wanted to protect their subjects-pony and griffon alike-from the ravaging menace of marauding dragons.

Indeed, in the final 30 or 40 years before the final fall of the Griffon Kingdom, Princess Celestia had finally come to accept the legitimacy of the Griffon Kingdom. It was only the chaos and anarchy caused by the collapse of the griffon monarchy (see above) that compelled Celestia to forcefully reassert Equestrian rule over predominately pony-populated territories that were previously under griffon rule and became part of Equestria once again.

Did the Apple family, or a large part of it, feel compelled to leave a territory that was formerly part of the Griffon Kingdom, becoming nomads for many years and several decades? That Granny Smith's own branch of the Apple family eventually settled in what became Ponyville (see the episode Family Appreciation Day) as a result of the collapse of the griffon monarchy?