The Byzantine don't have any unit that could remotely call themselves true spearmen. Pick a faction with the ability to train better spearmen than basic spear militia and the Mongols shouldn't be much of a problem, providing the venue isn't an open field.

The Muslim factions has good spearmen, pack them in narrow city streets and watch the horses die.

Some European factions can train Pikemen and Pike militia, these guys would absolutely slaughter Mongol cavalry.

Habidler and Swordstaff militia also fare well against cavalry, and also infantry.

And don't forget some quality archers, and you can also have a catapult ready to do some area damage, in the narrow city streets any unit hit with a flaming catapult ammo will have a hard time trying to continue the fight, ballistae comes as a nice alternative.