Here are two other spots that sound really interesting and would be great to check out. I've been to the Wildflower Centre in the early spring, so it was pretty bare, but I bet now it is full of interesting flowers. Neither of these are free and they are both out of the city centre. Ness gardens in the Wirral.
If these are too far, then I would love to just meet at Sefton Palm House (right near me) or Calderstones, which sounds cool.
I'm not able to join you all next Tuesday (July 21), but I will be ready for Tuesdays after that!