Don't do every single mission you can. I found focusing on the story missions with a few (only a few) side quests works much better at keeping one interested. Also the Heroics and a few PVP matches put together enable "easy-level-mode".
If you're finding the population lacking, think about re-rolling on a different server. I have done so multiple times.
PVP warzones are boring to me as well (I only use them to level).......the open-world PVP is however much much more satisfying.
In a lot of ways the game actually does 'begin' with level 50. While I've enjoyed the stories I have at least one character in each class at the moment (of course only one of my characters is a lvl 50) and it is obvious that once you reach 50 there are plenty of other things one can do.
1. Hunt for all of the datacrons.
2. get the crystals you need to perform the 'museum' missions.
3. get a complete set of both the endgame PVP and/or PVE gear. (this one has been keeping me occupied for quite some time now).
4. Find a guild interested in the high-level RAIDS and even inventing raids (ie. group up and take over a reb-controlled base/area just for the fun of it which trust me would be one hell of an achievement).
Again, if your server is too empty re-roll on another with more people. Don't worry about losing your character progression. A good solid guild more than makes up for that. You'll have guild mates sending you (or crafting it for you) the gear you need and running you through the FP's and Heroics which will level you back to your old level and beyond.
If you stay on a server with limited pop or guilds of course the game is going to feel like a grind and become a chore. Take action.