You will come out the back door of the Beach Club and walk alongside the lake (past the Yacht Club) towards the Dolphin. Then curve to the left, over the bridge... You can't miss it.
Oh wow, I didn't know there were any Space Center tours. Can you share a link to the tour company? When we were in Honolulu, there were ton's of tours that picked you up at your hotel. It was so nice not to need a car.
Easy pleasant walk, you can take the friendship water taxi's too but I think the walk ends up taking about the same time. Kennedy Space Center is great we visited on a trip to DVC Vero Beach once.