Its central location means you'll spend a lot of time using Salamand as your home base, whether you're headed for the Semitt Falls or the Snow Cavern.
Salamand
Hilda asked you to find Josef, and he is waiting in the northeastern building in Salamand. If you ask him about [Mythril], he'll indicate that it hasn't yet been recovered from the Semitt Falls. The other townspeople mention that the men of the town (Josef excluded) have been brought to the Semitt Falls as well. That's your next destination, but before moving on, take some time to explore the shops of Salamand.
If you thought the Spells in previous towns were breaking the bank, you haven't seen anything yet. Salamand has four Spells, all for 1,500 gil, and three of them are really good. You don't really need to have Teleport (which you can find in the Semitt Falls for free) and Warp, but Life is a must. Long term, you may want to purchase multiple Life Tomes so you can recover even if your main white mage dies. The fourth spell, Sap, is an MP-decreasing Spell that can be useful against certain Spellcasters. It deals only fractional MP damage, and is bugged so that it doesn't work against most late-game spellcasters, but it has its uses.
On the weapon front, the second-tier Sword, Axe, and Bow are available here, all for reasonable prices. All three can be found in dungeons later in the game, but better versions will be available for sale before then. None of the weapons is so compelling that you should switch what weapon types your Characters are using, but you should upgrade anyone's weapon when possible.
The only new Armor in town is the Bronze Armor, and the other bronze gear from Paloom and Poft can be purchased here as well. The Bronze Armor is strictly worse than the Copper Cuirass you could find in those towns, unfortunately. If you haven't upgraded the other pieces yet, now is a good time—unlike the weapons, you won't find any of this Armor as treasure any time soon.
However, there is one important consideration when it comes to armor, and that is the Evasion penalties it inflicts. This early in the game, your Agility and shield level are likely to be too low to provide much Evasion, and heavy armor will drop that amount significantly, maybe even to zero. However, you don't want to have too low of an Evasion score, because it will reduce the rate at which you gain Agility (and thus, more evasion). Even 4% Evasion doubles your chance of gaining Agility compared to 0%, and every 4 points increases it again. Right now, the Defense is probably worth the cost, but once you start getting into the midgame, you may want to consider lighter armor to help this vital stat grow even faster. (All of this also applies mechanically to any back row characters. Evasion may not help them avoid attacks that aren't coming their way, but it also helps determine turn order.)
To the Semitt Falls
The Semitt Falls are relatively close to Salamand as the crow flies, just across the mountains to the southwest, but reaching them involves a fairly long trip. There are two potential routes. The easier of the two is to head west until you reach a river flowing into the sea, then follow that river back east to the Falls. This route has the extra advantage of being half traveled on Canoe, where you will not be attacked. You'll want to conserve resources on your way to and from the dungeon, so the fewer battles you have, the better.
The other route is long and almost entirely on foot. Head south from Salamand and follow the mountain ranges southwest and then west. You'll see a lake to the north, which is the same lake where the Semitt Falls entrance lies, but that entrance is at the top of the waterfall and you're stuck at the bottom. Instead, continue west, turn turn north until you reach a mountain pass that merges with the river that leads to the top of the Falls. There isn't much reason to take this route, but it's good to know about if you get lost while exploring the world.