Oo the phone, one hopes? It's going to be so terrible but also so useful - there's probably only so much being vaguely attached to a superhero team can fix things up on that front.
As for the appointment...
She's good to take care of the appointment... not tommorow, because that's probably when they're going to do stuff about venom, but pretty much any day after that? Actually, she probably wants a day free of other commitments to just hang out and make sure she has her financial stuff worked out, honestly? And that should probably be before, if only to calibrate what amount of money is reasonably worth her time. So... somewhere from 3 days from now to when she goes to Themiscrya, if that works out, ideally, she supposes?
She'll do a bit of winding down - she'll do a final look over the lantern - looking good, honestly? Then she'll make a memory stone for general utility and/or more green light work later, and then make the blank for the little key and anchor for the lantern's subspace system, and then another, for another subspace storage project. She'll throw in a start for the budding process, too - it should be if anything more stable than the individual sparks, so even if he doesn't want to go that route and there's no special mechanism for 'saving' them, she can probably just do that.
She'll scare up something to read - she's sure by now there's some oldie but goodie asimov stuff on the web by now, and that sounds fun enough? She'll do that for a little while and then....
Alright, fiiiiine, before it gets late enough for it to be awkward she'll run over and set up the whole PO box affair. She'll have to fuss about the biometrics later if she wants to do more bioupgrades, but she'll cross that bridge when she comes to it. It's a little unforunate that there doesn't seem like there's much of a league bioguy, but she can scare that up later. Honestly, the most practical thing she could do would maybe be to copy something like red tornadoes body, but she's not quite that personally excited with transhumanism that she wants to be the first person to go through that sort of uploading process, and there's probably a billion things to figure out with all the technological changes that has happened over the years, not to mention magic and everything. And biological bodies are fun.
(She might as well ask the gift what generating a power for that would look like - could she get something for that elemental... tech?? that red inferno and red tornado uses out of the box? Making humanoid droids is definitely a path of all time to walk down.)
She blushes a little. She... was a little overenthusiastic there, wasn't she? She's kissed cheeks hello and goodbye before, but it's not exactly... normal for her to do it like that either, really.
Anyways!
Off she goes! Hopefully it has the phone and the rest of the stuff batman was setting up for her...?