Master Belch was the source of the zombie infestation in Threed, so you should go back to Threed to make sure all is well. When you go back through the graveyard passageway, you'll find that Threed is back to a normal daylight color, and the townspeople are out and about instead of cowering in tents and houses in fear. Good job!
Finding an Insignificant Thing
Before you begin the next part of your journey, check the drawers in the hospital rooms of the Threed Hospital. You'll find an insignificant item. This belongs to a man in the Twoson Hospital. You'll get a really good, rare item if you take it back to him: a Magic Truffle. It restores 80PP, making it the best PP-restoring item in the game. You don't have to get it now, but when you do get it, hold on to it for later.
Go through the Eastern Tunnel
Now that the ghosts are gone, you can use the eastern tunnel to get to the next destination. It's a long way to walk, though, so you might want to take a bus. There are a couple of bus stops in front of the hotel.
Once you go far enough, you'll discover a traffic jam. Apparently, a huge herd of buffalo are crossing the road, so nobody can go any farther. The cars are completely blocking the road, so you'll have to walk through the desert to continue on your journey.
Walk through the Desert
Stop in at the drug store. The trek through the desert will be difficult. As you walk along, each member of your party has a random chance of getting sunstroke. You'll know that someone in your party has sun stroke if you see a red flash from time to time. Sunstroke is kind of like poison, except it doesnt reduce your HP quite as much each time it affects you. Still, you shouldn't leave sunstroke untreated. It's easily healed with any of the healing spells (α, β, γ, Ω), or you can get some wet towels at the drug store--they instantly cure sunstroke.
Be sure to upgrade your equipment at the drug store, as usual. Get some poison curing items as well, in case you run out of PP to cure poison. Oh, and get some food if you don't have any.
There are a lot of items that you can find in the desert. However, you might want to wait until later to do that, since you'll get sunstroke a lot and will be assailed by tough desert monsters. But if you do decide to explore, look for the lost contact lens, the black and white sesame seeds, the talking bones, gift boxes, and more.
Finding the Sesame Seeds
The black sesame seed is in the northwest part of the desert. If you go northwest from the oasis that has four trees, you should find the black sesame seed fairly easily.
The white sesame seed is to the west of the miners' house. You can also go east from the entrance to the monkey caves and you should come across the white sesame seed.
Finding the Contact Lens
If you want the contact lens, find the gift box that is to the west of the miners' house, then go north from that gift box. You will pass a pile of bones along the way. You will see the sparkling contact lens after you have walked for a little while.
Continuing to Fourside
If you want to completely avoid monsters, and also avoid sunstroke, you can hug the tops of the southern rocks of the desert. If you walk so you're touching the south rocks, you'll discover that you don't sweat while you're there, meaning no sunstroke. Also, very few monsters hang out around there, and those that do can be avoided by making them get stuck on cactus and things like that.
At the eastern part of the desert, you'll find a small shack with a miner standing outside. Give him some food. You can sleep in his shack, and use his phone to save the game.
By the way: once you reach the miner's house, the buffalo stampede will be gone, so you can go west on the road if you want. The only thing of interest there is the gift box with $1,000 in it, and the slot machine. The machine itself is broken, but the Slot Brothers (Pincho, Pancho, and Tomas Jefferson. Not Thomas: Tomas) will do the slot machine thing for you.
If you're ready to move on, though, then go east through the tunnels to Fourside.