From what I could find, the areas that you can only access or are expanded after obtaining the National Pokedex/entering the Hall of Fame in Emerald are:
Areas five and six of the Safari Zone, a new cave area where Steven can be found in Meteor Falls, Southern Island (But only if the player has an Eon Ticket.), Trainer Hill, the Battle Frontier, Artisan Cave, Desert Underpass, Marine Cave, Terra Cave, the S.S. Tidal, the Trick House, Altering Cave, Birth Island (Only if the player has an Aurora Ticket.), Birth Island (Only if the player has an Old Sea Map.), Navel Rock (Only if the player has a MysticTicket.), and Route 103 (Adds Altering Cave).
Source: Going on Bulbapedia's pages for each of the locations in Hoenn and using F3 to search for things related to obtaining the National Pokedex.
Also, how do Gyms change after getting the National Pokedex?