Another way is to go to SkyScanner and put the destination as "Everywhere"
I just assumed that you were in NYC (given your username) and thought I'd play around to see the most cost effective way to 6 sectors. I also assumed that you wanted day returns, given time constraints. I therefore used Saturday January 12.
If you only have 1 weekend (assuming that it is weekends you have off) consider looking at two one way flights. As much as I tried to convince various booking engines to give me 3 segments both out and back, they all insisted that you could only do two on the return. But if you book separate reservations then you could so something like:
for $111, overnight, and then COS
for $126. (Total: 237)
If you can't take two days consecutively, then there are some pretty good deals on day returns on Saturdays from what I can see on that date. I guess you could do a simple roundtrip, plus a second one with a stopover.
For example I got LGA
for $138 and LGA
for $156. (Total: $294)
Obviously you couldn't do them both in one day, but you get the idea. Doing these short east coast trips would obviously be much cheaper than 20,000 miles. You're looking at Australia for that sort of mileage.