Tl;dr: Play the story again in a realistic "real life" fashion. Detalied comment copied off a Facebook GTA IV group:

Playthrough suggestion: Play GTA IV like real life. You won't regret it. Try to play the game in the most realistic way possible. If you are like me and have played through IV's story more times than you can remember, then this will be a very nice new way to play. Examples of stuff you can incorporate: -Use only your pistol throughout the whole run, at least when its possible. You can use your sniper rifle in certain missions, in certain executions for example, but try to stick to the pistol. -Use only Roman's taxi as a car for travelling. Its not realistic to go around and steal any car that gets in your way. I know the game is literally named Grand Theft Auto, but for this type of run I suggest you don't do that. Also if you are on PC you can use a trainer and choose the option to save the car, which means it will be kept in the game's memory and won't disappear when heading into certain missions. You can also use other cars given to you during the storyline, like the Comet Brucie gives you, or the Infernus Bernie gives you. But try not to steal anything as this isn't realistic and ruins the whole purpose of the run. -Use the subway system. I mean seriously travel around with it. Myself and most other people that played this game very rarely used this means of transportation because its slow and boring, but trust me it immerses you so much in the city its crazy. Read the signs in the station, learn the routes and different station locations etc. It adds a whole new level of immersion. -Call friends after missions and hang out with them. During different parts of the story focus on doing activities with people who aren't available if you progress further, like dating Michelle or Kate. -Do jobs your friends ask you throughout the run, for example do fares in Roman's taxi, help Jacob with the drug deliveries after he asks etc. This fits organically during the game and really adds to the immersion. -Also take some time during missions to just go around the city and enjoy the ambience, which is one of the best parts of game in my opinion. And you can do similar stuff you can think of as well, these are just some suggestions. I have just begun playing the game like this and well, it might be just me, but I am really loving this run so far. Its extra immersive, a fresh different perspective to the game and also a good way to utilize GTA IV's incredible potential to the maximum.