Lindblum is one of three major kingdoms (and cities) located on the Mist Continent of Gaia in Final Fantasy IX. It is the epicenter of most major technological advancements in the game, including the use of Steam power instead of Mist. Lindblum (the city) is massive, having three separate districts dividing it: The Theater District, known for it's theater and home to the group Tantalus; the Business District, where all the shops and inns are located; and the Industrial District, where all the technological work and experimentation takes place.
The castle of Lindblum is suggested to be the largest of all three kingdoms. As the party first arrives, Steiner remarks at the massive size of the Airship dock, located directly within the castle, and that "even Her Majesty's Red Rose could fit in here". The castle itself is divided into 3 parts (like the city): Base Level, where there are gates leading to below the Mist and to the Harbor; the Mid Level, where there are guest rooms and access to the rest of Lindblum; and the Upper Level, where the Regent's throne room and conference room is located, as well as the boiler room and access to the roof and telescope.
It is at this point in the year where the annual Festival of the Hunt, a large celebration in which the entire city is run amok with various beasts that competitors kill for points, is underway, and Zidane, Vivi, and Freya all participate (and award the party a prize, depending on the winner).
The Theater District is home to three screens. Upon entry by the cable cars, the party will find a small little plaza, where you can run downstairs to the Tantalus hideout, or enter the artist Michael's house to find a few items (as is the case each time you return to the city). In the second screen, you can continue down stairs to the Theater or visit the Tantalus hideout, where there are several chests containing gil and the occassional rare item. The final screen finds the team outside the theater, where a group of Lowe Groupies reside, screaming with joy over their favorite actor, Lowe (who can't handle the attention and fame). This last screen is eliminated when Alexandria attacks the city on Disc 2.
In the Business District, you can buy all the items and weapons that you need. This is the only access point to the outside area of Lindblum above the Mist. There is the Inn as well, where you can rest for a small fee. Up further is a fork in the road, one direction leading to the local church (which is destroyed by Alexandria in Disc 2), the other to the item, weapon, and synthesis shops. Alice runs the Item Shop, Dragoo runs the Weapon/Armor shop, and the Synth shop is run by an old man and his apprentice. With each pass through Lindblum (in the story), the Synth shop becomes more and more adequate, where the apprentice goes from too weak, to too strong, to (finally) just right.
The Industrial District is the location of a few homes and a bar, but not much else. You can visit the pub, or meet with the engineer in the final screen, where he is working on various experimental technologies, such as steam power. You may also find a few items in his house. This entire district is gone after Alexandria attacks in Disc 2.
After Queen Brahne and Alexandria attacks Lindblum, certain areas of the city become unavailable (thanks to Atomos and the Black Mage army), namely all of the Industrial District, the church area of the Business District, and the theater screen in the Theater District. You no longer have access to the areas for the rest of the game, though you can see the progress of rebuilding as the story goes along. Alexandria occupies Lindblum until Brahne's death.
Throughout the game, Lindblum is the central hub from which all plans and major actions are decided or begin at. From checking up on Burmecia, to heading after Kuja on the Outer Continent. Lindblum is at the right point to access either Alexandria or Burmecia, making it a strategic location. The kingdom itself has many other areas within it, such as one entrance of Gizamaluke's Grotto, Qu's Marsh, and Chocobo's Forest.