I too, hate PVP.
I still play EVE, though, due to loving sci-fi and spaceships in particular.
I too, though, want a PVE-only experience in EVE.
Here are the rules I have learned to follow to avoid PVP:
(1) Avoid PVP-oriented areas: stay in highsec.
Lowsec/Nullsec revolve around PVP 24/7.
Therefore, if you want to be PVE-only, you have to treat lowsec/nullsec as if they don't exist.
No exceptions. "Rewards" (often scams) do not matter.
Even risk/reward does not matter.
You're PVE-only. Low/null do not exist for you. No exceptions, ever.
(2) Avoid wardecs (and taxes): start your own one-man corporation.
This both shields you from wardecs, and avoids the up to 10% tax charged by being in someone else's corp (including NPC corps, which tax at 10% of your income from missions, the primary PVE activity). As a side bonus, it makes you less visible (which is what you want, as PVP players tend to consider PVE players as nothing more than prey/food).
If you do get wardeced anyway, drop to an NPC corp for a little while, then reform your corp with a new name. This costs the wardeccing corp at least 10x more than it costs you to delete and reform your corp. Thus, only someone who absolutely hates your guts is going to continue to wardec you after you pull this trick once.
(3) Avoid suicide ganking: don't fly ships with expensive modules
People suicide gank you for two reasons: to steal your modules, or just for fun.
If you avoid having expensive faction/deadspace/officer modules, it isn't profitable to suicide gank you in highsec.
(4) Avoid talking to people: most EVE players are not friendly to PVE players
Many PVP players consider PVE players nothing more than easy targets. Food. Prey.
Some will attack you simply because they hate the idea of people doing PVE in the game.
Don't tell anyone that you are a PVE player. Don't talk in local or chat channels.
In general, don't talk to anyone at all. Treat EVE like a single-player game.
Other people don't exist for you in-game. By all means get your info from the web, but never talk to anyone in-game, and if you must talk to people on forums, ALWAYS use a disposable forum alt character to do so. No matter how much they bait you, never post with your main or reveal their identity. Their words cannot hurt you, but their missiles sure can.
Given the ratio of merciless PVP players to nice PVE folks, speaking up (aka: making yourself interesting, and therefore a target) is NEVER worthwhile. Example: Once, saying I only play eve for the PVE got me added to someone's kill-on-sight list, even though I said it in a chat channel dedicated to PVE play.
(5) Avoid being near people: use the starmap to find less-populated systems
Even showing up on someone's overview can make you a target. Make it a goal to live in a system with level-appropriate agents, and very few human players.
(6) If you must interact with people: run incursions
Incursions are high-end PVE content. They can be lucrative, e.g: 50m ISK per hour.
And, unless you're filthy rich in EVE, you won't have the most valuable ship in the incursion fleet you join, hence you won't have much to lose (relatively) by joining them.
The downside is that such fleets often have approved lists for ship fittings - if you can't fit exactly what they're asking for, you can't join. So, training up, buying the right ships/fittings/etc, can take awhile.
(7) Avoid being targeted/scanned: move quickly
Don't autopilot if you can avoid it, especially in 0.5 sec systems that border lowsec ones.
(8) Read around
Almost all PVE risks (and ways to get unexpectedly PVPed) are well documented.
Know how they work, so in the event of an emergency, you know what to do.
You don't want to take the risk of undocking with an active wardec, no matter how unlikely it seems they'll be waiting for you. Because, knowing EVE, they probably are.
(9) Don't fly anything you can't afford to replace
I must admit I've violated this rule myself at times, but by doing so, I've come very close to losing everything I owned in EVE! I only escaped that fate by being lucky. You might not be so lucky.
So, don't fly any ship you can't afford to replace.
(10) Insure your ships
Sometimes insurance is worth it. Sometimes, it isn't. Still, in general, especially when you're about to do something risky (like run a new class of mission) you should opt for more insurance.
All of the above rules were born out of actual mistakes I have made as a PVE player, and what I have learned from them.
It can be lonely playing EVE as a PVE player, due to the inability to interact with other people.
Still, EVE is a very predatory world. By playing a PVE player, many people will automatically classify you as prey. So, it can help to adopt some of the strategies that real prey use to avoid being hunted, such as:
be almost impossible to notice (hide away & keep quiet)
once noticed, be "not worth the effort" (be a hedgehog, not a pig)
once attacked, evade, rather than fight (birds don't fight cats on the ground, they just fly away)
don't risk anything you can't afford to lose (if you can't replace it, don't use it)