Well, the classic "oh hey deep place" as far as 2kki is concerned is the Wataru sector. It's really big, kind of dark, but it features some of the best art in the game and a really cool atmosphere. You can get there by going to the Neon City, where there will be a subway tunnel east-southeast of the entrance from Square-Square World.
Other places not as well heard of are the Star Ocean and Rusted City, accessible from Atlantis, the Forest Carnival sector (Starting with Dark Forest) accessible from the Gray Road, the Red Rock Caves, a single world accessible from Red Streetlight World, and more. Really, the only tips I can give you are to look around the wiki and look for connections you haven't found yet, then go check out the worlds they connect to.