After defeating Alexander, the party will emerge onto the Archylte Steppe, a huge open area full of nasty monsters. Don't underestimate the enemies here - many of them will annihilate your party when you first arrive, and some remain dangerous or even impossible to defeat until after you finish Chapter 11 and return at the end of the game. Coming here also opens up missions, the primary sidequests of Chapter 11 (and indeed, the entire game). Whether you choose to complete missions for a while or advance the plot immediately is up to you. You can complete the first 17 missions before moving on to Mah'habara, if you're so inclined. (You can also unlock Mission 54, but it is likely too difficult at this point.)
After you complete Mission 14 (which in turn requires finishing Missions 01, 02, 03, 05, 07, 12, and 13), you will be able to ride chocobos on the Archylte Steppe. In addition to being a speedy form of travel, chocobos will help you avoid combat. They have three "morale" points, and touching any enemy except an Oretoise will drain one of them. (Touching an Oretoise will cause the chocobo to immediately drop you off and flee, so be careful.) Expended morale points return in a little while, and if all three are lost, the chocobo will leave you behind. There are a number of areas only chocobos can go, marked with yellow circles. In addition, you can dig up items all across the Steppe. The items you can dig up are listed as treasures for the Central Expanse area, even though they can be found just as well in most other areas of the Steppe. Each time you enter the Steppe, five chocobo digging locations will be activated. It is beyond the scope of this note to explain the exact details, but the locations are not completely random, instead being chosen from a set of possible locations. The ultimate prize for chocobo digging is a Ribbon, which will be the 20th item you dig up. You can continue digging up random items indefinitely, however.
A few notes on monster appearances in the Archylte Steppe. Cactuars will not appear until you encounter one in a cutscene on a cliff in the Eastern Tors, after which they will appear in several areas. If you encounter a Cactuar and let it perform its Cactus Dance without attacking, it will Grow into a Giant Cactuar, and then perform an Encore Dance and Mature into a Cactuar Prime. This is the only way to encounter these enemies. Finally, once you complete Missions 56–62, Adamanchelids and Adamantoises are replaced with Shaolong Guis and Long Guis, respectively, in all areas where they appear. (You may also have to complete Mission 51, the final mission of the Faultwarrens, though I cannot confirm this.)