Here we go!
High Sec Anoms
These are everywhere, they are very easy and even new players can run these. They have names such as Hideaway, Den, Burrow, and Refugee, each faction space has these, and they can be run with T1 fit destroyers. Each site has the potential to drop faction loot or spawn Escalations which are DED Concord sites that have the potential to give expensive Deadspace loot.
High Sec Exploration
These sites must be scanned down using a ship designed to do so. These are Data/Relic sites and require a module called a Data/Relic analyzer to run these sites, the loot can go from useless carbon to expensive modules/blueprints.
Missions
These range from Levels 1-4, and each mission tier requires a bigger ship. Level 1 missions can be run by T1 fitted Destroyers, level 2's require a cruiser minimum, level 3 requires either a full T2 fit cruiser and or battlecruiser, level 4 requires T3 cruisers or battleships. Each mission gives what is called loyalty points, these LP as they are called can be used in the faction store to buy expensive modules/ships/blueprints etc which can then be sold on the market, plus the missions themselves give "bounties" which at a higher tier can be 900k-1.1mil per NPC kill.
Abyssal Space
Certain tiers of Abyssal space may be accessed from high sec space, these pockets of what is essentially abyssal deadspace are three rooms, in which you kill the NPCs in each room and then the loot cache, which drops items you can then sell on, the higher tier i.e Tranquil being level 1 onto calm and then agitated, the higher loot pool and the more money you will make per run. You can buy these Filaments on the market.
Incursions
These are high-tier fleet activities which move around high sec space chasing the "incursions" These are sites where fleets run for Concord LP which can then be converted into large amounts of ISK, the ship types required will vary on which group you are running with, there are public fleets you can join for these, but I am not sure of the names.
Mining
In each system, there are "Asteroid Belts" which contain basic ores in high sec such as Veldspar which gives tritanium, as you move down the system list i.e from 1.0 sec to 0.5 sec, the ore being spawned in these belts becomes more expensive. You will also find frigate based npcs in lower end systems, so defence is key.
Cosmos Missions
There are what is called "cosmos" chains, this being said, a lot of them have been removed or are just plain broken, again this being said, a lot of the chains are still intact, where you go from each agent to agent, along the way finding modules you can sell, blueprint rewards which are worth a decent amount of ISK. But as I said, be warned, some cosmos chains are just plain broken.
Epic Arcs
Epic Arcs are mission chains ranging from 45+ Missions to 50+ missions where you can go from agent to agent and get greater and greater rewards in ISK etc as you go on, they often end in a massive standings boost and or high-end implants which can be sold for a large amount of ISK, these arcs I THINK reset every 30 days. So can be run at least once a month.
So there you go, a full list of PVE activities available to you in high-sec space - As you move down to 0.4 - 0.0 space, the same activities are available with much higher rewards.