What I would like would be something close to 4th edition essentials, but with the ability to have fights without a battle map.
In my opinion, the martial classes in Essentials reverted to something like their original conception ("I hit it with my sword") but gave options to make the character more interesting to play ("I hit it with my sword while using the 'poised assault' stance, rather than my 'battle fury' stance, meaning that I get a +1 to hit instead of a +2 to damage.")
I like the at-will, encounter, and daily powers for the wizard (I'm not crazy about it for non-spell-casting classes). The wizard should have a greater variety of spells to choose from, and perhaps should have new AW/E/D spells for each level of advancement. There should be "useless spells", as well. The wizard should have to acquire spells from scrolls and such, rather than automatically gain them when he advances to a new level, I think.
For ability scores: random rolls shouldn't be punished so harshly. I read once someone's description of the 0e rules concerning ability scores; it was pointed out that a fighter with 10 strength was about as effective a fighter as one with 16 strength, although the latter fighter would gain experience more quickly. I like that idea, and getting rid of the "+1 to ability checks for every two points of ability" in favor of a flat +1 for ability scores 15 and above, and a -1 for ability scores at 6 and below, and getting rid of the increase in ability scores every other level, would make rolling for random ability scores more popular. Rely on experience levels to increase a character's capacity for adventure rather than increases in his ability scores. Make the character have to work for increasing a particular score (push a boulder around to increase STR, like in Nethack), or find a "Tome of Physical Conditioning", or something.
I also like the idea of splitting up the game's components like the BECMI did.