Minako's world interactions post has the majority of what I plan to do with her, but here's another list of things I'd like to offer as chances for CR.

Exploring with Koromaru! She and her puppy will mostly be in the Supercenter, enjoying themselves and trying not to feel depressed about everything that happened at the end of Persona 3. It's her first world hop, so she'll be more interested in indulging in everything it has to offer instead of info gathering. She's more than happy to do things as a group!

Info gathering! Despite all the time she's going to spend having fun, she's not opposed to helping with research. You just have to ask nicely.

Sparring and practicing with magic! She has barrier magic instead of summoning powers, so she'll be trying everything she can to improve her skills as soon as possible. Volunteers willing to let themselves be boxed in are very welcome. Also, she doesn't want to get rusty with her spear, so she'll probably find someplace quiet to put in some PT time. If she doesn't get in trouble for it.

Talking about androids! Wanna hear about one of her best friends who was an android that was slowly turning more human? She will happily talk about Aigis if you're curious. Guaranteed way to get a rank 1 Social Link with her (๑ゝ◡◕๑)