Hello!  I’m getting ready to run my first ever campaign in a few weeks and I wanted to ask for some advice about a side quest.

One of the quests is for the characters to find and capture a town guard who was discovered to be working with some local bandits.  The guard is fleeing because he knew the guard captain was on to him and also the bandits would kill him for not accomplishing the task they wanted him to.  Rather than have the PCs move tokens around on a map I wanted to set it up as a skills check and only use a map if they finally track the deserter down.

I’m looking for suggestions on a procession of rolls they could make beyond the obvious go-to of having the ranger check for tracks.  Some ideas I had would be to let them question other travelers, or make perception checks to let them find snags of cloth on a branch, or see smoke from a distant campfire, etc.  Any suggestions would be greatly appreciated, thanks in advance!!

I think the ideas you've already come up with sound pretty good, but how about questioning around town/looking for a trail leads them to a tiny hamlet or farm, where the locals are covering for this deserter (maybe he is a local lad).  The party could then decide whether to question the residents, sneak in at night - or just decide that they are lawbreakers and should be arrested.  Up to you whether they find the deserter there, or find that he's been sent somewhere else to hide by the locals. 

I think that would help you flesh out the quest beyond some skill checks, and hopefully give your players some fun roleplay to get into when they are deciding how to track the deserter down. 

That’s solid, I like that thanks!  Tracking him to some allies who would want to protect him would let the party make intimidation/deception checks and add some variety to the rolls.

Just have the party watch this and roll investigation.

Seriously, unless the quarry is some sort of Rambo type with high adventurer level type survival and escape evasion abilities, most fugitive hunts end "close to home".  Have the characters spend some time around the barracks, maybe interrogate some bandits who know what he was up to to get to the know the fugitive.  Those leads will give the PCs leads based on the bonds and network the fugitive has.  Maybe the personal office of the guards has notes on next of kin if the fugitive died while in service, things like that.  

It's possible the fugitive then is "hiding in plain sight" living in a refuge community.  If the desertion is more fresh or a hot trail, and the fugitive and their sanctuary has passed WIS checks, more likely the fugitive will be kept up in a cave or trappers cabin or something but still receive some sort of material and social support from the sanctuary providers.  This could be done through charming up the inhabitants or surveillance.  

Even those fugitives who have no one still tend to lurk near society in a dumpster diving capacity.  And those with the actual Rambo skill set who don't get caught often die of untreated injuries incurred during flight (received either from the environments or pursuers).

I had a similar scenario in my campaign recently, only it was a PC who stole an item and deserted the party!

I had come up with a general idea of how the PC got away. He snuck away in the night and retraced the party's steps along the way they had gotten to their campsite back to the riverbank. There he met an ally who ferried him across the river by boat. Then he took an airship.

Then I just let the players make decisions about how to track him and asked for the appropriate checks based on what they attempted. I didn't have a preconceived idea about what ability checks they'd have to do and how many they'd need to pass. They have a ranger who aces every survival check, so it was no problem to track him to the riverbank and discover that a boat had pulled up on the muddy bank. Their initial thought was to follow the river and look for a boat. But I had them make a perception check to notice boats docked on the opposite bank. Upon crossing the river, they found muddy footprints going from the boat to the airship dock. They spoke to the personnel at the airship dock and found out a person of the PC's description had boarded an airship bound for the city of Rian. But the airship crew was in league with the PC and had falsified their flight plan. The PC actually went to Edhilonde.

Subsequently the party ended up helping a rebel, who in return offered to have her contacts look for any info on the PC. This allowed them to discover his last known location, and eventually led to him.

In general, imagine yourself as the deserter guard and use your wits to think how you would get away. You know that they will send a tracker with good Survival ability after you, so think how you can thwart someone looking for tracks. Maybe you lead them off track and then backtrack, walking away backwards. Maybe you cross a fallow field and then pay the farmer to re-plow it. You also tell him that you will return with more money if you aren't caught to incentivize him. So when the party comes asking questions, the farmer will say he saw nothing. You might need an Insight check to catch him lying, and then a Persuasion or Intimidation check to get him to confess. Etc. Come up with what happened first, and then mostly improvise how that affects the outcome of the players' actions.

You could do this as a skill challenge, but I think skill challenges are better suited for urgent ticking clock situations. The only difference between a skill challenge and normal role-playing is that each player has to take an action every round. When you are on a mission that will span several hours or days, it makes sense that the character with the best Survival bonus will always do the tracking, and the character with the best Charisma will always do the talking, and any player with a clever idea should pipe up when they have it, not wait for a turn.