Improving Garen
The champ is pretty terrible because it's trying to be a Darius and failing rather badly at it. The obvious fix is to differentiate him from Darius.
That is, he should be a vanguard that is durable and reduces damage taken by his allies while healing from timing skills to absorb large hits. While Darius wants to snowball fights, Garen should be about strangling fights out by frustrating burst attempts against his team and winning by attrition.
Garen has a garbage laning phase for 3 reasons:
1- His sustained damage is pretty bad (the less problematic part) 2- No in-combat sustain whatsoever. His passive has got to be one of the most gimmicky garbage in the game and should be changed. 3- His villain mechanic is terrible. It should function like Kindred's mark, at lv6 Garen assigns a villain and that triggers a 30 sec cd between changing villains.
Key changes
Garen's weakest skill by far is his W. Until it's scaled up, it's quite terrible as an active skill of its own. Compare this to Irelia's W or Fiora's parry or Vladimir's pool or Riven's shield+leap or Urgot's shield. Point being, as a mitigation tool this is quite a horrendous ability with an even worse cd.
The obvious fix is to reduce the cd on it and make it a 50% damage reduction for 2 seconds that makes you CC/snare immune and lowers the attack and movement speed of those that hit you while it is up.
Then we should look at Judgement. Remove the ridiculous penalty on multiple targets hit; Darius doesn't do less damage when an axe hits multiple minions, why should Garen be completely screwed by the presence of minions or teammates in a teamfight when using his main contribution to a teamfight?
Furthermore, this ability should not do less DPS than autoattacks until several rank ups. Scale it up.
If Garen channels the full duration of Judgement, he should be healed for X% of the damage dealt by Judgement after the final tick hits an enemy champion.
As far as the Q and ult, they could seriously use animation reductions. I can't count the amount of times the ult constantly fails to land because of how long it takes to go off. Q's movement speed should always be active upon activation, not wear off after hitting someone with Q.
I actually don't think Garen needs initiation/gap closers. Bruisers should stay heavily countered by proper ranging; Darius is just an anomaly with his ridiculous pull, but I don't want bruisers to counter mages and ADC's because mages and ADCs should be the counters to bruisers while bruisers counter any melee who engages them such as assassins or fighters.
I might even suggest that the ult needs changing because as it currently exists it's just a way worse version of a Darius ult without the reset and way more ramp up to using it even against a villain.
I would look at Kayle or Lulu's ult for inspiration in terms of making him an immovable object that highly supresses all damage, including true damage, during the ult and radiates tenacity to his team.
In essence, make Garen a defensive counterpart to Darius where he's focused on retaliation and frustrating dives against his team by making him really hard to remove if he times his W and ultimate+E right and ends up winning the war of attrition.