Ok... [SPOILER WARNING]
Purity Forest and Joyous Tower are both unlocked the same way. You get access to them both after you reunite the Lati@s and have the Sky Blue Plains friend area. To do that you have to buy the freind area Southern Island and Have HM Surf. After that you can go to the Northern Range then find Latios. After that you can then go to Pitfall Valley to rescue Latias... after this both Lati@s will join your team.
Now after you do that... you can head over to Whiscash's Pond and find Team Meanies and do missions for them until only Ekans is left. Then you go over to the Pelipper Bulletin Board and look mission from Medicham. Wish Cave should be unlocked now.
Hope you could follow that
. Anyways best of luck