You don't define "soon." AA miles do not expire for 18 months, and you can pretty much keep them indefinitely if you have just one transaction in your account every 18 months. So, you may want to consider just keeping the account open as you may unexpectedly add a few miles somewhere down the road and end up with enough for a free ticket.

Of course the Hilton option is quite attractive for short-term gratification.

Happy New Year and welcome to FT!