From level 10 on there are lots of things - particularly Mirror event than level you at super speed

But getting to 10 is a slow boring slug - anyone know ways to get to 10 in 2-3 hours?

Assuming you don't like doing Story Missions - based on your statement - get yourself an XP Boost and do Patrols. With an XP Boost 1 patrol would probably give you close to 1 level.

Patrols are only 780xp - each lvl is about 2800xp

That's no more than four for a level. They're like popcorn. Eat them up.

But unlike popcorn, once they are finished you can do them again lol

If you do the following missions ("Stranded in Space", "Diplomatic Orders", "Hide and Seek", "Stop the Signal", "Researcher Rescue", "The Kuvah'Magh" and "War is Good for Business"), you should get to Level 7. (without the XP Boost, you'll, of course, have to do less missions).

Once you get to Level 7, you can get to Level 50 by doing nothing but Duty Officer missions.

Yes, but this is not the "quickest" way as the OP has asked.

I thought it might've been one of the quickest ways since one can choose 20 different assignments. If possible, take the ones with the highest XP. With that, you'll probably hit Level 10 in a few days.

At that level, you don't have enough doffs to run 20 assignments. In fact, I'm pretty sure you don't even get your first set of doffs until you hit level 7 or 8. It doesn't really compare to doing missions. Your typical diplomatic doff assignment gives 50-70 CXP for a 1 hour assignment, and maybe a couple of hundred XP. Doing a story line line mission, which only takes 20 min, will give a couple of thousand XP. At the early levels, you pretty much gain 1 level for each mission you do. So doing 3 missions back to back will take you up 3 levels in 1 hour. Doffs won't nearly do it as quickly.

Now, if you are talking about leveling while being offline, well that's a different story.

Get a VA to drag your ass into a mirror event.