My story requires that my characters travel south. This is necessary for my story because I need the northerners to see how the southerners live. However, although it's necessary to my story, I haven't thought of any reason for it to be necessary for the characters. I ask that you all just say the first thing that comes into your minds when I ask this, maybe your ideas will get my creative juices flowing: Why did they travel south?
Widespread flooding/storms/forest fires/earthquakes left them without a home, so they headed in the first direction they thought of to try to rebuild. What setting? Is this on Earth, present day, Europe? Or is it a fantasy or S/F set on another world or alternate reality? Knowing these things may help us channel ideas.
Fantasy, based on Europe. I'm not sure of the age yet, this is another problem for me. In some ways I want it to be like the dark ages, in some ways I want it modern. I'm not sure yet! Their home has not been destroyed, I just want them to travel south temporarily, then return home. It's kind of a reconaissance trip, but I'm not sure why exactly.
They've heard a rumour that something they want is to the south/they've run out of it in the north. I don't know enough about them to know what this might be. If they're religious it could be a relic/shrine. Could be for resources and commodities. Could be land to expand.
well, people have been stealthily invading their land (not in a violent way though) and the face of their land is changing. They don't like it and want to drive the newcomers out. The newcomers are from the south, so my protagonists travel south for some reason. I'm not sure why, maybe to see what they're up against? I don't know yet.
Crop failures due to recent bad storms have left the area in economic trouble, so this group is heading south with durable goods and marketable skills. They plan to trade for food and shelter, and for seeds to start next year's crops.
Perhaps they don't want to start a war with the invaders so they head south to see if they can find a peaceful way to stop the invaders from taking the land. If you do want the characters to start a war, then perhaps the characters can be a flanking group that travels south to attack the capital and then heads back north, sort of like a guerilla group. This seems a little excessive to me, but it's up to you.
This is more the kind of thing I was thinking of. I'm not sure though, my protagonists are not particularly peaceful, most of them would be more than happy to drive the newcomers out by any means necessary.
Since you're talking about Europe, I think of southern farms with lush sunny pastures and plenty of crops and fields of grapes. I think of pretty young women who have hiked their skirts up and are crushing grapes with their bare feet in wooden tubs. When I think of the North, I think of Norway with its majestic fjords and cold rocky shores. The sky is overcast. The landscape is a bleak mixture of mist and craggy rock where cottages of thick stone squat in defiance of the elements. Historically, this is one of the reasons why the Norsemen became Vikings raiders.
Northern land is attacked by Neo-Nazis, so to take refugee your travellers go to the Southern land. Or, the Northernland is afflicted by some bacteria, but rumors are that the Southern land has a possible cure.
Maybe they're assassins, aiming to chop off the head of their enemies? Maybe they're fulfilling an ancient prophecy! That always seems to work when a proper explanation isn't available. Maybe the Gods have ordered them to go south, but they aren't sure why yet. That'll give you some time to start writing and decide on a reason later. Maybe they're being lured into the trap of a false peace deal, which turns out to be a way for the enemies to get some hostages (depends if they are important people or not, politically).
Whatever options you consider, I'd suggest a choice that compels them to travel, rather than a choice that beckons them to do so. It increases the conflict and the stakes, making a stronger plot.
Cog has a point, that necessity dictates conflict. And he is 100% correct. Making the trip necessary makes for strife just to make the trip. (Grand example is the movie "RV") But, you have not put that forth that they "need" to do this, but more of a "They want to do this" type of deal. So think of your mood and why you want them to do this. Do they need to do this or do they want to do this. Business/Pleasure? Answering things like that will help you discover a more exact motive which would fit better in your story.
A group of gypsies from an oppressed culture, who have formed a band and want to spread the word about their lifestyle to other countries?
All the reasons I can think of immediately: Invasions; To experience the world; Bored of the same place everyday; Kidnapped, maybe by some villain; Mission, king sent them out or something; Exiled, due to being framed maybe; Disease/Some sort of exodus; Lost and wandered; Destiny/Prophecy; Vacation; Elope, or just running away by themselves; Job, become a sailor or weaponsmith; Training, personal training possible; Searching, like for someone/something, or new method of irrigation, or simply for fortune; Weather, tidal wave washes characters away while sailing, or floow washed characters into river; Rescue, save someone/something; Drafted to War/went to join war; Religion, like a pilgrimage; Trading, crops, livestock, etc.; Discovery, gold mine, or the likes; Marriage; School/College/Study; Magical Doorway, like a portal or teleportation device/spell, they accidently fall into it; or you could make them start in the south and try to return home instead. Any of those reasons spark an idea?