American Airlines (AA) is a founding member of oneworld, with hubs in Dallas Fort Worth, Charlotte, Miami, Chicago, Phoenix, Philadelphia, and Washington. Searching American’s own award space is the easiest job on this page, because you do it right on aa.com with a free account and no miles required.

Go to aa.com and log in to your AAdvantage account, or create one for free.
In the flight search box, enter your cities and dates and tick Redeem miles before you search.
Results show award pricing by cabin for every flight. American uses dynamic pricing, so the same route can swing a lot by date. The calendar view shows the cheapest dates at a glance.
Watch for Web Special fares, which are discounted awards only bookable on aa.com. They are often the best value, though they don’t allow changes as freely.