If you serve the tzatziki immediately, you will have a pleasant contrast between the crispiness of cucumber and softness of drained yogurt. Leaving the sauce in the fridge for a day or two will soften the cucumber, giving a more uniform texture to your tzatziki. It's very tasty anyway :)
Serve the tzatziki with raw vegetables (carrots, tomatoes, cucumbers ...) or grilled ones (like eggplant, zucchini, onions ...). And of course don't forget some bread, pita will be perfect.