Christmas trees:
There is an NPC in each nation in the port area (so Port Bastok, Port Windurst, and Port Sandy). The one in Sandy is near the airship agency entrance (Elvaan); the one in Bastok is called "Tree Talker," and is by the fountain in the big square (Galka); the one in Windurst, near the gate to Sarutabaruta (Mithra).
Talk to the NPC; s/he will ask you to fetch some supplies from one of the Market Moogles near the MH entrances. The NPC will tell you which one to go to (there's a Market Moogle in each area of the city).
Talk to the Market Moogle, who will give you a rare/ex item, take back to the NPC. There is a time limit on this quest--what the limit is depends on how far the Moogle you need to go to is. If you completed the quest within the time limit, the NPC will give you a tree. If not, s/he'll send you back out.
You can only do this quest once per game day.
Edited to add:
Kid presents--from what I can tell so far, giving kid presents allows you to teleport to other cities. If you talk to the Moogle that first gave you the Smilebringer quest while wearing the Dream Hat, he will offer to teleport you to one of the other two cities. If you've accumulated enough 'joy' (that is, handed out enough presents), he'll teleport you to the city. If not, he'll tell you you've been slacking off. Once you've teleported, your 'joy' goes back down--that is, you need to hand out more presents to be able to teleport again.
Outpost Teleporting!: if you trade the teleport NPC 10 (I think) sparkling hands, s/he'll teleport you to any outpost, regardless of your level and whether you've done a supply run there. Not sure if there's an NPC who's selling/handing out fireworks or if you just have to buy from AH/crafters.
