Lucy because she was by far the easiest to get to. Good luck if gold is your goal, though. (Imagine my rage when I found out that she doesn't appear until the tenth iteration after getting to 57 rooms cleared.)
Reflections on the others:
Spenser's facility has a unique concept, but I'd say that the Palace tests your luck far more than the Pike ever will.
Arena...oh god, this one was a nightmare. I eventually reached and defeated Greta, though. Lost in the first round of the fight immediately afterward, but SO WORTH IT.
Battle Pyramid has a fun concept that includes scrounging for items and weighing the risk of battling a Trainer against the reward of the information they might offer as well as increasing the radius of illumination. However, I have stumbled across layouts where every exit from the starting room is "guarded" by a Trainer, though the fact that they only have one Pokemon each helps. Brandon is also fun to fight because of his tossing legends in your face.
Tucker...again, a pain in the ass to beat. I reached him multiple times on level 50 but never won, then tried open level, more or less aped his lineup, got the matchup advantage and won handily. I then kept going and lost in the finals of my seventh tourney. The amount of prep work involved for each battle makes this facility very stressful.
Noland was fun, Factory is fun if rage-inducing, but if you're satisfied with just silver, it's not that bad. (Open Level is the way to go here, as they're all fully evolved.)
Anabel...I don't have an opinion on her, because I'VE NEVER FREAKING REACHED HER. Got to battle #34 once before falling apart in the face of a Gyarados.