Sleeping Dogs: Definitive Edition

Every time you go up a Face level, 1 through 8, a new item can be bought in stores that increases the amount of Face XP you get. None of these conflict with the full set bonuses like Triad or Cop XP, so every time you go up a level, go get the next upgrade.

Level 1: Beaded Dragon, Chain, +5%, $750. Found at Number One Clothing, the shop in North Point's Night Market that you have to go in during the tutorial.
Level 2: Hang+Sui Leather Wrist Bands, Bracelets, +5%, $5,960. Found at J. Jiggler in North Point, northeast of the Night Market and south of Kam Chuk Overpass.
Level 3: Ikoze Sport Watch, Watch, +10%. Found in a lockbox at Victoria Peak. Zoom in all the way on the map and it's just to the right of the K in Peak.
Level 4: Frisky Blockers, Glasses, +10%. Found in a lockbox near the Undercover HQ. Alternatively, find the parking garage northeast of Denlau Alley and the lockbox is just east of there.

Favors and dates are two good ways to get the face meter up, but one good way of getting a lot quickly at this point is to do the martial arts clubs. Follow the guide for that particular achievement and it should take you from level 4 to 6 rather easily without any face bonuses. Note that if you follow the guide to the letter and use the Bronze Statue costume, you won't be able to equip any of the above bonuses.

You can get to Face Level 5 very fast by completing favors (all around the map), drug busts and other open world events. By completing these events you gain Face, a type of XP in the game. If you go for the Mr. Nice Guy achievement, you'll definitely get to Face Level 5 before you unlock it.