Personally, I would like to see the Pokedex, Pokegear, Pokenav, Poketch, and Start Menu integrated into a single full-color touchscreen interface. I say call it the Pokemon Digital Assistant.
As far as layout
Main Menu with the following Icons:
Pokedex Pokemon Items Trainer Stats
Phone Radio Applications Settings
I think the Pokedex interface should be a combination of the FRLG and DPP interfaces. In addition to Pokemon Information, it should also contain an encyclopedia of moves and integrate the Fame Checker into a 'Important people' database. The pokedex should also include tools for calculating weakness/resistance and determining mating compatibility.
The Pokemon Option works similar to its DPP incarnation, but also allows you to remotely check the stats of Pokemon in storage, and Happiness has a display within the stat screens.
Items should use the same categories from DPP, but separate Held Items into a seperate category. To make navigation, instead of each category consisting of a long list of items, display them on a grid, with line breaks to separate subclasses and have all items organized in the a preset order.
TM and Berries would be listed in order, 15 to a row.
Held Items might have one row each for incenses, type-specific boosters, signature items, Weather Extenders, Plates, Choice Items, Power Items, etc.
Trainer Stats works like the existing Trainer Card. The recent Pokemon and PokeRadar Apps should be integrated into the Trainer stats.
Phone works identically to Match Call in Emerald. Also, you can register the Daycare and they will call you when you have an egg to pick-up, and you can call them to check the levels of your Pokemon
Radio works like it did in GS, but has been updated to a Full Soundtest with all of the game's music.
Applications is for the small stuff that does not fit into the other 'Top Level Functions'
Map - Combines Berry Map, Town Map, Marking Map, etc into a single utility while adding other functionality.
Scheduler - Combines the Memo Pad and Calendar Applications into something that is actually useful.
Probability Tools - Spinner, Coin Toss, etc.
Settings works similar to previous games and also allows you to customize the appearance of the PDA.
As for the Clock: have the PDA's main menu display the time and date along the top edge. Any Poketch Apps I did not mentioned should be integrated into larger, more full featured applications.
YES YES YES YES!
This is what we need: to have the touchscreen actually used in an efficient manner (instead of just buttons like those in the Bag in DPPt), in full color, and as a substitute for the menu. I was actually going to post something similar, but then I saw your post.
IMO, touchscreen implementation in battles was excellent in DPPt (separating the items, making you choose moves/items with the touchscreen, etc.) but was lacking outside of battles. Sadly, given these are remakes, I think this is too much of an update for it to happen in HGSS, but I'm hoping it does in future generations.