Convincing a partner to be more or less affectionate in public isn't easy, but it can be done.
Check out the following strategies:
Open up: Talk to your partner about what makes you uncomfortable about PDA. Ask what they can handle (a hug, a kiss on the cheek, an arm around the waist, a hand on the knee, etc.) and don't go beyond those limits.
Compromise: Bring a 'touchy-feely' partner down to your level, or a 'hands-off' one up by coming up with less obvious ways to be affectionate in front of others, such as holding hands under the table, sharing a look, or blowing a kiss across a room.
Get playful at home: Tickle, wrestle, kiss and be spontaneous when you're alone. It just may carry over to the outside world.