You can search for award availability on ba.com for the cities you want. It will ask you to include partners and once you click the include partners button it will show you the choices.

Most times the site is buggy or it does not pull up proper partner availability. You can search for milesaver awards on aa.com and if there is availability, I believe you should be able to book it using ba miles. If ba.com does not show the same availability you can call the ba service center to book.

Slightly unrelated, but another nice aspect is for awards within 21 days aa charges fees if booked using aa miles (in case you get the citi 75k aa card also), but ba does not ($75 savings).

thepointsguy.com has a great write-up on BA miles and the BA dashboard on flyertalk has great info too.

Hope that helps.