So open up your imagination for this, too much for me to actually draw, maybe someone with the time and energy can give it a go.
Figure a park the size of Disney World. But at the center of it all, instead of a castle, is the Hall of Justice. The building can be as big as needed. A section could have a multiplex theater showing various DC movies animation and live action. Main entrance would have on display as in the comic, the uniforms of the JL, and can include really any uniform from heros to villians through out the years. There can also be a auto garage section of a collection of Batmobiles and other super hero / villian vehicles, that one can take photos in. An a section for a restaurant , DC themed of course, could even be like the new Gotham Restaurant that is supposed to open up some place in Europe. An of course other additions to buy misc, shwag and comics. Various offices could be put in off limits to the public that could be used by actual DC writers / artists etc. An other offices available to rent for hosting private business events etc.
Everything else in the park would be your DC Roller Coasters / Rides, Themed Rides like Disney has with its destruction of Star Wars. The themed rides can be taken right out of any comic, pick your favorite, could be a tour through Arkham Asylum, or Park Row, or a tour of Smallville.
Instead of disney characters touring the park, you have your superheros and villians. On top of that, there could be choreographed , interactions between heros and villians in the park itself amongst patrons. ( instead of a typical disney parade ) . Winter could include an ice rink and winter could kick things up with your Ice Villians… why not, and some where for the summer time can be a water park. Which would of course be an Aquaman theme.
Spring time you could have a green themed area, with plenty of foilage for poison ivy, or swamp thing, maybe a butterfly area, in the mix. Penguin is a bit of bird guy, so you could also include an avian section, with trained birds , or birds that kids can interact with.
An of course, over charge the snot out of anything and everything as all theme parks do.
Throw in some parking garages and shuttles , a hotel or two, have a nice day.
I’d rather go to this type of theme park, than a disney , or six flags.