Go to the School area and click on the black rectangle where the clock or bell would be, that brings you to the School basement.
Go to the Museum and walk downstairs, that brings you to the Crypts by walking instead of Map warping.
Go to the Auction House and walk upstairs, there you can become a 'member' of the club.
If you have built them then go to your House and walk upstairs or go out the back door and walk to the bulkhead.
Go to the Desert square just before the Caves and walk, do not Map warp. You will be in an unmapped area that does not do anything.
Walk into many of the sub-maps instead of Map warping into them. There are many transition areas but most don't do anything.
none of these are really secret.
there are 4 'hidden' areas related to the Kings quests, 2 in the Haunted Forest, one in the Lost City and one in the Mountains.

The Invisible Isle
The Store Basement
The Hidden Forest
The Secluded Valley
The Haunted Lake
The Deep Swamp
The Southern Jungle
The Brilliant Cavern
Are these secret ares too?