LHR isn't the problem; unless you have a flight originate in the UK or a connection over 24 hours (in which case you will pay the UK Air Passenger Duty tax unless you're flying out of Belfast, it's a transatlantic award portion using British Airways and its onerous YQ surcharges.

Look at available one world routing and schedules using innosked's interactive one world network route map and schedule: http://onw.innosked.com.

Look at the Milesge price chart on aa.com (being aware mileage rates will generally increase 23 Mar 2015):

Read the following threads here:

https://www.aa.com/i18n/AAdvantage/r...tner-chart.jsp

and

http://www.flyertalk.com/forum/ameri...es-2015-a.html;

for assistance, use: http://www.flyertalk.com/forum/ameri...iscussion.html