You can bid farewell to any sub-heroine whose route you have finished (seen the 100 Aff events). The route is unlocked after you complete their subquest and talk to them to have sex once more. The original version of the game didn't have the routes (but had the subquests) but the DLC added them, your screenshot says "Summer Memories+" so it has the DLC.
The secret base is part of Akari's route, you do her route after completing the Menko sidequest.
You won't have sex with Yui until the 80 Aff event so minimum you'll need that, but it's possible the sex stat events don't unlock until you finish their routes, I'm not sure about that. There's also a 100 Lewd scene you'll have to see before the 200 Lewd one happens.