I made the mistake of opening up new regions to explore by spending 8 power points a piece. Now I just realized that all of my power points are spent and the main quests still require 20 to 40 power points. I have closed all but two rifts in the Hinterlands, and only have a few quests available in the Hinterlands.
What is the best method of quickly and safely obtaining power points, excluding fighting extremely dangerous enemies?
There are a lot of other free or cheap areas that you can get points. I've only unlocked a few things so far to get to skyhold, but now I am up to over 90 power points from just doing side quests in hinterlands, storm coast, fallow mire and crestwood. Hinterlands is the only area I've cleared of missions, the other areas I just bummed around in briefly. I always look at my map to see where missions are when I get to an area and try to string them together to save travel time (hardly use my mounts).
Haven't unlocked any areas in Orlais besides val royeaux.
Worst case, the "requisition" quests are infinite. I found the storm coast requisitions to be very easy. Each requisition you complete gets you a point and you could farm that to infinity AFAIK.
Besides the Hinterlands, you can also get power points in The Storm Coast, the swamp area, and the desert area in the beginning.
Later in the game there are additional places that you can earn them.
You can buy influence from a merchant in Skyhold. Each "tome" gives you 1 power regardless of the price, but the amount of influence you receive changes depending on the price. This is probably one of the fastest ways to get more power.
You could also close fade rifts in different areas because for each fade rift you close you get two power so you can unlock more areas and get more and more power and build everything up
