I use a similar strategy to ghug- another property I look for is keeping the numbers in a snake of decreasing value - the biggest is the bottom right, followed by decreasing numbers up to the top of the right hand line, followed by decreasing numbers down to the bottom of the first line in from the right. You can be more relaxed about this on the third and forth lines, or near the bottom of the second line. But, if the first 6/7 numbers aren't following this snake pattern, I focus on bringing them back in order (which you do by merging in to them, not by moving them around).
This strategy means that if you have a choice between merging up/down or right, you should generally merge right (which means you don't have to think as much). I also do everything I can to make sure I always have four numbers on the right - so I'll ignore matches if I'm down to 3 numbers on the right, hoping to spawn a number in the top row.
Using this strategy, you should be able to pretty consistently get to 2048, as long as you don't make a misstep in your merging right instead of up/down, and as long as you're never forced to merge left.