As a holder of lots of BA Avios, I've found that my only realistic near-award access into Europe with them is on EI metal through DUB. (Disclaimer: I've never actually seen an Air Berlin aircraft, let alone one with award seats on it and a routing that enables me to easily get to and from it.) So while BA could be an option, it's ironically not a very good one for anything actually related to BA metal from the U.S. I think if I really wanted to go to London with my Avios, I'd be buying the DUB-LON segment on my own.

ex-DFW with about 60k per person to spend and a desire to do some travel in premium cabin, I'd probably be looking Central/South America.