If you just want to log on and do your dailys as fast as possible, Metrica Province is the place to go.
Healer (X / 10 Allies Revived):
The reactor in the top left corner of the map contains a lot of dead NPCs. Closest waypoint is Survivor’s Encampment Waypoint.
Kill Variety (X / 13 Types of Enemies)
The same reactor also contains a lot of different mobs, ripped from their home by the unstable magic of the reactor. If you don’t get to complete the daily variety kills here, you should be well on your way.
Events (X / 5 Events):
Events are pretty much everywhere on the map and fairly easy to find. Just outside the reactor, in the area between the Muridian Waypoint and Arterium Haven Waypoint, there are three events, some of them with veterans.
http://wiki.guildwars2.com/wiki/Metrica_Province#Events
Veterans (X / 5 Veterans Defeated)
When you do dailys they often involve killing veterans. Sometimes, inside the reactor, events pop up where you have to kill one. Then you get to kill two birds with one stone.
Aquatic Kills (X / 25 Underwater Kills):
There are several places with water in Metrica, most of them contains critters you can one shot. In the water at the Old Golem Factory Waypoint there are a bunch of Salmon and Crabs and easy to kill yellow mobs.
Crafting (X / 10 Items Crafted):
At the Desider Atum Waypoint you have crafting stations where you can complete the daily crafter and also, as we all know by now, get access to the bank if needed.
Daily Kills (X / 50 Kills)
This you obviously don’t need to stay in Metrica to complete but when you have done the events etc you should be more or less done.
Gatherer (X / 20 Gatherings) & Dodger (X / 15 Attacks Dodged):
Like the Daily Kills you don’t need to do those in Metrica, especially if you have a higher level character and like to run Orr for better tier mats. Same with dodger, that you should be able complete while doing the other combat related dailys.
Daily Laurel Vendor (X / 1 Laurel Vendors Visited)
Go visit a Laurel Vendor, there is one in each city. Job done.
Welcome to Metrica Province!
You could argue, and a few people have, that WvW is a better place to go for your dailys and while its a good place to go, this post is about getting them done as fast as possible. Having 10-15 dead NPCs lying there waiting for you to save them, where you in the same area at the same time can get the Daily Variety Kill more or less done and being able to one shot critters under water while not being worried that a zerg of <Insert Server Name Invader/Defender> will steamroll you, is in my opinion faster then doing them in WvW. 
Edit: I realise that there will be new dailys soon (today? tomorrow? next patch?) which probably will make this tip obsolete. But there it was, taking up valuable room in my brain, so I thought I’d throw it out there. And as far as I know, the old dailys will not be removed, only new ones added.
(edited by unum.6209)
