DCA-TPA-MIA-ORD-DCA for $176 available some days in September, for example 9/13, 9/20. TPA is about the same price for four segments, for example DCA-PHL-TPA-CLT-DCA for $175 on 9/20.

I find these with google.com/flights. Put in DCA,IAD as the departure city, leave destination blank. Put in the same day (example 9/20) for the departure and return. Put in Oneworld in the airline drop down tab. Look at the map for cheap cities. Then look at the calendar to find the cheap date and then the flight schedule and see how many segments.

Try different dates, usually a Saturday that is not a holiday weekend is a good starting point.