Tested a few different things, based on the math it looks like you should max out your space with Flower Bed's first then upgrade to Arcade Cabinet 2 to maximize happiness with the space you have, if you aren't going for achievements or unlocks.

Park:
Level 1: $600 total (Happiness 5)
Level 2: $600 previous cost + upgrade $1200 = $1800 total (Happiness 10)
Level 3: $1800 previous cost + upgrade $1800 = $3600 total (Happiness 15)
Level 4: $3600 previous cost + upgrade $2400 = $6000 total (Happiness 20)
Level 5: $6000 previous cost + upgrade $3000 = $9000 total (Happiness 28)
$9000 / 28 happiness = $321.43 per happiness

Arcade Cabinet 2:
Level 1: $750 total (Happiness 5)
Level 2: $750 previous cost + upgrade $1500 = $2250 total (Happiness 10)
Level 3: $2250 previous cost + upgrade $2250 = $4500 total (Happiness 15)
$4500 / 15 happiness = $300 per happiness

Juke Box:
Level 1: $750 total (Happiness 5)
Level 2: $750 previous cost + upgrade $1500 = $2250 total (Happiness 10)
Level 3: $2250 previous cost + upgrade $2250 = $4500 total (Happiness 15)
$4500 / 15 happiness = $300 per happiness

Old Couch:
Level 1: $600 total (Happiness 4)
Level 2: $600 previous cost + upgrade $1200 = $1800 total (Happiness 8)
Level 3: $1800 previous cost + upgrade $1800 = $3600 total (Happiness 12)
$3600 / 12 happiness = $300 per happiness

Flower Bed:
Level 1: $125 total (Happiness 3)
Level 2: $125 previous cost + upgrade $250 = $375 total (Happiness 6)
Level 3: $375 previous cost + upgrade $375 = $750 total (Happiness 9)
$750 / 9 happiness = $83.33 per happiness

Hay Bale:
Level 1: $60 total (Happiness 1)
Level 2: $60 previous cost + upgrade $120 = $375 total (Happiness 2)
Level 3: $180 previous cost + upgrade $180 = $340 total (Happiness 3)
$340 / 3 happiness = $85 per happiness