Guadosalam, as you have probably guessed, is the home place of the Guado. It's also got a few other features, as you'll soon find out.
Before you do anything you'll be introduced to Tromell Guado, one of probably many servants in Seymour's service, and also go through a short tutorial on customizing equipment, which Rikku allows you to do. The door pretty much right next to you leads to the Inn where there's a Save Sphere for you to use if you so wish. Check the right-hand side of the manor before you go inside for a Mega-Potion. O'aka is in the equipment shop, so now you can actually see why you should always buy from him — his weapons are better and for the Yellow-series of armors that help protect against lightning-based damage he charges 1000 less Gil! There is also an Al Bhed Primer XIII located within the room to the left of Seymour's manor, with the Guadosalam blitzball team. It'll be on the ground right next to the giant tree trunk growing within the place. There is also a chest containing 3,000 Gil behind this tree. The layout of Guadosalam is weird, so it'll take a while for you to get used to it.
Anyway, you were asked to meet Seymour, so head inside the manor. There is a chest upstairs hidden behind the stairway. It contains 2 Hi-Potions. Talk with everyone to learn a bit more, then approach the downstairs door to trigger Tromell to reappear. You'll be taken to a banquet hall, where there's lots of food (that you can't eat). Talk to everyone in here and Tromell will reappear, shortly followed by Seymour. You'll see a little of Zanarkand as it was and Lady Yunalesca, the first person to beat Sin. After some more shocking developments, you'll regain control of Tidus and you'll be off to the Farplane. Not in the sense that you just died, but actually heading up to the Farplane. Just inside the entrance on the left is a chest containing 8 electro marbles.
Continue ahead into the Farplane, but Rikku and Auron won't go inside. Talk with Wakka, Lulu, then Yuna.
After a few touching scenes, you'll head back down to Seymour's manor to speak with him. If you look around, on the mini-map there's a door-less dead end on the middle floor which has a chest containing an Elixir. Attempt to leave Guadosalam via the Thunder Plains exit, and Shelinda will show up, telling you that Seymour went to Macalania Temple. Better hurry back and tell the others then. Once you're done back at the manor, you can also go back to the Farplane for the Venus Crest in a treasure chest on the left side when you enter, as well as listen to a guy talk to his sister, and have a small chat with Lulu, then you can head down to Thunder Plains.