Many of us split dosages of T3, but it's pretty rare to split dosages of T4, such as Synthroid. I've been told that splitting the dose (of T4) can help keep the TSH from becoming suppressed, but don't have personal experience with that.
Typically, when splitting dosages, you'd want to space them evenly during the day. The first dose would be taken when you first get up in the morning, with the second dose taken somewhere around early afternoon. Of course, this will depend on your schedule - for instance if you don't take your first dose until 10 am, you'll want to take the second dose later in the day, while avoiding taking it late enough to affect sleep.
You'll need to make sure you have an empty stomach when you take your Synthroid. The dose taken when you first get up would be no problem because you'll be waking up from a night's sleep, when presumably you'd have an empty stomach. . Be sure to take it first, with a cup of water, then don't eat/drink anything (besides water) for 30-60 minutes.
The second dose should be taken in the same manner but could be more problematic, depending on when you eat snacks/lunch. Because food inhibits absorption of thyroid hormone medication, you should arrange your schedule (snacks/lunch) around being able to have an empty stomach.