My two cents here...it's what i would like to see, but not what i expect.
-Carry over save games from SR3 so our choices in story line and things we did/didn't do carry over.
-More diverse character customization in relation to the actual build of the body itself (full slider sets like we have with the head) so we can go into more depth with the body of our character.
-A return of gangs from the past in the form of allies or foes.
-More story content (a LOT of the SR3 missions were nothing but intros to the mini games and it left the actual campaign content feeling a little light).
-Full reign over both cities.
-More gang customization (outfits, gang types, vehicles, cribs, etc.).
-The return of Big Willie's Cab Company being accessible with the cell phone (I miss the Big Willie call message from SR2).
-Co-op increased to 4 players (since you can have up to 4 homies with you in game as is).
-Increased character interaction during campaign content (the random dialogues during some of the missions was pretty awesome).
-More mission content that makes full use of the different vehicle types (watercraft were somewhat neglected in SR3 compared to land and aircraft).
-More instances of singing along with songs on the radio...badly.
-Finally having love interests made available for the player character be they existing characters, new characters, or a mix of both.
-Increased quality of the PC version (SR2 was a horrible PC game in terms of how it ran, and SR3 was a LOT better...hopefully SR4 will be the best PC translation in the series yet).
-Mascots and Bikers added in as full-fledged gang factions with their own story content.
-The return of the shopping malls (raising hell in the mall in SR2 was a ton of fun and I was really bummed that there wasn't a mall in SR3.
-More accessible interiors (places like the Gothedral and the Burlesque club would have been nice places to check out).
-More effort put into the strip clubs and the fact that hookers were everywhere. GTA IV did a better job at portraying strip clubs and prostitutes than a billed "over the top game" like SR3...which is kinda sad since those parts of GTA IV were pretty terrible.
-More things to do in the cities. Let us have things like bowling, pool, illegal street racing, underground fight clubs, and other activities that would most likely be happening in the city anyway.
-Extended vehicle customization (SR3's vehicle customization was great and I hope they expand on it.
-Custom vehicle creation (give us set of parts that can be mixed and matched so we can create our own custom vehicles that we can show off to and buy/sell/trade to our friends).
-Dynamic day/night cycles.
-Bring back and expand on the hand-to-hand fighting styles from SR2.
-Bring back environmental interaction (I miss clubbing people with parking meters).
/$0.02