If you're bored of the good ol' fashion way of leveling an alternative method available to you is participating in Space Battles. Space Battles are a truly unique feature which you will only ever see in this game. They are kind of like a rail shooter, if you've ever played one of them. Your ship is controlable but only to a certain extent. While you are able to fly around and avoid rocks and other obstacles flying all over space on your own is not possible.
At first there is only a single space battle available to you but as you level up and advance further throughout the game more and more Space Battles will open up. Each of these battles is repeatable as many times as you want but as you could imagine it is not really that good to constantly grind them over and over. It is smart to do at least one a day though, depending on what quests are available to you via the Command Board to the right of the Galaxy Map. A picture of where the Command Board is can be found below.
Every few levels a new space battle will become unlocked and chances are the mission for it will be available at this board. At level 25 there are at least 6 different space battles that I am able to participate in. I made a few different videos of these battles and also took a few screenshots to give you an idea of the variation you will be experiencing. Note that these screen shots are from The Republic side so if you're looking at them as an Imperial, you could be slightly confused.
Below each of these pictures for the Space Battles you can also find videos that I made for each one and uploaded to Youtube. As I do more Space Battles I will be sure to upload them as well and post them on this guide page.
This is the first Space Battle that you will come across. The initial reward for this Space Battle is 10k xp with an additional reward of 2.6k xp each time you do it after the first time that is at least until it becomes gray to you and no longer rewards xp. This mission is so easy the only thing you really need to know is to avoid the rocks and anything else that you can run into... Which is quite obvious anyway.
Do this battle inbetween Taris and Nar Shaddaa
Do this battle inbetween Nar Shaddaa and Tatooine.
This is a question that I expect people to be asking often since the whole Space Battle thing is new to everyone. The thing about Space Battles are, while they're fun and quick to do they don't really reward all that much XP. The first one you do each day (The daily) does actually reward a good amount of xp, usually around 10k each day you complete it. Also each of the first times you do a Space Battle for the quests they reward good XP, but after that I can't honestly recommend doing them unless you're seriously extremely bored.
I do, however recommend doing a Space Battle inbetween each of the planets. Generally inbetween each planet a new battle is unlocked and a new quest appears for said space battle. If a quest appears for a new space battle I do recommend doing it just because it will award a large lumpsum of XP.