Keep the chocobos and other mounts outside. First and most important reason being the crowding. Chocobos are huge in game if you havn't noticed. Imagine a bunch (or even just 3 or 4) of people mounted on chocobos all crowding around the guild leve counter or the repair npc or in doorways or standing on top of people trying to bazaar.

Second is lag and stuttering. Cities are already generally laggy enough due to the volume of people all in one spot. Now give all those people gigantic yellow birds to race around with and someone's graphics card is going to have a heart attack.

Third, and this is my opinion, but there really isn't a need for mounts inside cities at this point. The cities are large, but are laid out in a way to where you can get where you need to go quickly. To sum up, I would rather walk than deal with the lag and crowding.