Where would the RO want to go on a date for a off day of the league?
Well, Chapter 4 kind of answers this, being a free day and all, but...
Ignis loves the quiet, but if she can be unrecognized (so, with her League collar), she loves going to stores. She didn't get much of a chance when younger to just have normal people fun, so taking her to the mall so she can walk through the aisles, see clothes and everything else, and then topping it off with some restaurant food inside the place would be a pretty kick-ass day, if you asked her. Just be with her as she pretends to be normal, that's all she wants. There's also... one other thing she likes, but you'll learn more (and perhaps even participate, if you're lucky) eventually.
Lat is a total home-girl. She doesn't say no to parties or anything, but she can get that whenever she wants. A good snooze-day with her 'person' where they watch a bunch of movies from the 80s and 90s (she likes Jackie Chan :p), stay in their pajamas the whole time, and eat whatever is easiest to make and eat on the couch would be her kind of date. Miss Kitamura wants to relax. Aki's a bit more complex, because she's never really been on a date before. She'd be up for basically everything the MC suggested, because she just wants to experience things with the person she cares for. You can go all the way from hiking to a day-long horror movie marathon with popcorn in your rooms and she'll be ecstatic. She just wants to be together.
Now, Nova does require an answer, because he does spend his free day in Chapter 4 doing a bit of an errand, but it's not that far off. He likes animals a lot, so he'd like to go to the zoo. The country he comes from has carnivals pretty often, and he likes those as well, so if the stars align, he'd like to take the MC to one. Forewarning, though, he's not very keen on many of the... Zipper-like rides (the ones that basically tell gravity to get screwed), so he's more likely to take you through the stalls and get you all the prizes on the second try. Mars really likes the ocean. He'd take the MC to the beach, and maybe go scuba-diving. The whole water pressure and everything helps with his super-hearing, too, so it'd be doubly relaxing, since he has his partner and can give them his full attention as well. After that, well... he's the most traditional of the ROs, so he'd likely have a reservation at some high-end place for dinner. You did what he liked during the day, so it's just fair that he spoils you during dinner.
Thanks for the ask, anon!