Neeko works as a mage jungler similar to Taliyah, Morgana, Zyra, etc. Having played many games with all of them, I can say Neeko is a solid B-C tier jungle. Every part of her kit helps her as a jungler. Note - Just make sure you know how to play kiting junglers! If you don't know how to kite in the jungle Neeko will clear poorly!

Why does Neeko's kit work in the jungle?

• Q - low cd, low mana aoe ability that rewards multiple hits if you hit a large monster and the target stays still. This is perfect for the jungle and allows you to farm quite quickly.
  
• W - swiss army knife for jungle. Not only does the passive give you sustained manaless damage and a slight movement speed increase for easier kiting, but you can use the active as an escape tool, a defensive scouting tool to prevent counter jungling, an offensive scouting tool when counter jungling, a shield for turret hits when ganking, a diversion for your ult, and a tool for jungle sustain. The last part is done by timing the W such that it collides with a monster right after an autoattack or one of your other abilities damages it. The timing is tricky but if done correctly the monster will aggro to your clone while you continue damaging it. This will not only absorb hits from the monster(s), it will also kite them away from you, preventing a decent amount of damage.
  
• E - helps you kite and damage camps, but mostly it is a strong gank tool. Similar to taliyah, morg, zyra jungle, your ganks are dependent on you landing your skill shot CC. Alone it is usually enough to force someone out of lane and maybe secure a kill, but if you can clip a creep with it (which is often the case ganking a pre-6 lanes) the kill is very likely.
  
• R - transitions you from a decent farmer with the odd gank to an incredible ganker and teamfight initiator. When combined with W and passive, this makes lane ganks very hard to survive, and skirmishes into full blown teamfights with your team having the advatange. In addition this is a strong counter jungling/counter objective taking protection tool. It's very hard to force a 1v1 fight on you, at herald or dragon for example, when you have your ult up. At worst you will escape with the long CC, at best you will kill them.
  
• Inherent glamour (passive) - the strongest tool in neeko's kit, truly made for a jungler. It is tedious, but this is key part of neeko jungle. Unlike laning where you don't have many opportunities to use this without being obvious, you should almost always be in disguise if you can manage it. It does several things. It makes tracking you difficult because there is always a guess whether it is you or a laner who has rotated. Before objective fights and jungle skirmishes, this can initially confuse the opponent but more importantly mask your health, making them unsure whether or not they can take a fight. You can bluff high health to force them to back off of a scuttle or bluff low health to bait them into a fight you'll know you'll win. Finally always disguise when ganking for the same reason. At best you'll get a bait, at worst you'll surprise the opponent with health or skill they weren't expecting.

• Pros - Fast, safe, & healthy clear, decent ganks pre-6, very strong ganks post-6, transitions into great skirmish and teamfight asset mid-late game, good use of passive allows you to gain advantages you otherwise wouldn't on another character.
• Cons - Squishy, skill-shot dependent, cannot solo objectives as well as other junglers, no through-wall dash means you are vulnerable to junglers who can avoid your CC like Elise and Olaf.

• Electrocute - Take either this or dark harvest. They are similar, but electrocute is more reliable early damage, and your early to mid game ganks are where you want to shine. Some people recommend predator on neeko jungle. I don't like it at all as it works directly in opposition to your passive since it alerts the enemies.
• Cheap Shot - Obvious pick.
• Zombie Ward - I always take this on mage junglers. Often your team will be less likely to be ward clearers, so take this responsibility. If you focus on vision clearing, it makes your ganks better, makes you resistant to counter jungling, and it gives your team stronger objective control. Ranged junglers have the advantage of safer ward clearing, so I prefer this over ghost ward or eyeball collection.
• Ravenous Hunter - You can take this or relentless. Ingenious isn't really necessary because you only have 1-2 active items that aren't super integral to your play. Ultimate isn't necessary because your R has such a low CD anyway. You could take relentless instead primarily for better ults but I find with nimbus this isn't necessary and Ravenous helps with early-mid objective sustain as well as teamfight sustain (since you're in the thick of it after your initiation).
  
• Nimbus Cloak - This is simply used for your ult. Chilling smite does not break your passive disguise. You can walk up, charge ult, and smite them for an easy way to get in range.
• Waterwalking - This one is optional. I like it because it helps with scuttle and objectives. One alternative could be absolute focus, because since neeko has such a healthy kiting style clear, this will be active pretty often and just makes you farm better. Another is gathering storm which will surpass both of these for longer games.
  
• Stat runes - Take atk spd and adaptive over 2 adaptive because that little bit of speed helps with kiting and makes your W better.

• Stalker's blade w echoes & sorc boots - obvious core on any mage jungler.
• Twin shadows - your first item because it is a farily cheap item that synergizes well with your ult, helps you gank, and gives you vision coverage for objectives.
• Optionals:
  • Morellonomicon - opponents have healing
  • Liandry's - opponents have health
  • Banshee's - opponents have magic damage
  • Zhonyas - opponents have physical damage
  • Void Staff - always good as 5th item
  • Death Cap - great final item if you have nothing specific to counter
• Trinket/wards! - Crucial part of playing any ranged jungler! Since you are taking zombie ward, it is paramount to swap to red trinket and buy one control ward on your first back. You are moving around the map and benefit from remaining hidden more than the rest of your team, so do this job and scan constantly, even between camps. Try to always make sure dragon and herald areas are clear of wards. In a perfect world your support would keep dragon warded, but this is rarely going to happen. So it falls to you. Control ward dragon after your first back and for the rest of the game always make sure to replace that ward if it is cleared. As a jungler you always need to know if they are doing dragon so you can contest or use the opportunity to focus another objective if you can't.

• Blue Side (Bottom) - Red -> raptors -> wolves -> blue -> scuttle and/or look for gank -> gromp.
• Red Side (Top) - Blue -> wolves -> raptors -> red -> scuttle and/or look for gank -> golems.
• First back - On your first clear, you want to back when you have at least 1025 gold. This gives you stalker's blade, boots, and a control ward. Do NOT try and skip the control ward. It is the most important item you can buy on your first back as it will give you crucial information on dragon.