The light cast by two 60-watt bulbs in a room that size is not very much and it won't much matter where it's hung in terms of overall illumination because the room will be dark regardless. I'd choose to hang the fan where it will do the most good moving air around and plan on additional lighting.

Even if the lights are limited to 60 Watts, you could use LEDs with a much higher equivalent light output. And, of course, you could also follow kudzu's suggestion.

You definitely need more lighting as stated above. Our family room is similar to your room and our fan light has 4- 60W equiv LED's (topside) plus 3-40W equiv LED's (downside behind glass) and the illumination is just nearing adequate for general low-level lighting. The fan circulation will do best hanging from the center of the room, and IMO, that is the priority location for a fan/light combo. Do use a long down-rod, our 6' down-rod places the fan at about 10' and it circulates well.

The consensus is that the down rod should be sized so the bottom of the fan blade is 9' from the floor. Article.