Space Heroes and Super Spies: The Miranda Lawson Thread

Because she made a deal with Mordin to record everything and release it on the extranet for $$$.

Seriously now, as a Miranda fan:
The engine room represented neutral ground, without the complications of her going up to Shepard's cabin (which looks like Shep is the one with the power) or him coming down to hers (he is patronizing her). Either way, he holds the power and she is catering to it. Neutral ground eliminates that - especially neutral ground of her choosing.

Why the engine room as neutral ground? Maybe Miranda felt threatened by Tali, who was quite obviously crushing on Shepard. (Kelly Chambers comments on Tali's attraction to Shep, and if Kelly had put it in a report to the Illusive Man, Miranda would have seen it. Kasumi even comments, "Really? The engine room? Right where Tali works?" or similar, implying other crew might have noticed as well.) Perhaps as a shot at Jacob, who Miranda had an affair with, and who could also see into the engine room. (Though when playing BroShep, Jacob is a decent guy and says it would "take a better man than him" to make Miranda happy, indicating he's truly over it and wishes the best for her on a personal level.)

Practically, there was no other place the encounter could be staged without BioWare introducing a part of the ship that hadn't been seen before (assuming you have all DLC and recruited all squad-mates).

I view the choice of the engine room as another sign of Miranda's insecurity with herself. The power dynamic that she struggles to maintain is a part of how she has traditionally valued herself. She knows it is a false standard, but it is Shepard who shows her an alternative. I don't think Miranda would have ever asked Shepard for help in ME3 (because that would be her admitting she's not perfect) without romancing her in ME2 and continuing it over to ME3.

That's my take on it, anyway.