"Don't split the party" is a mantra for dungeons. It's perfectly fine to split the party in a city environment, and that sort of thing happens quite often in the Dark•Matter game I run.
I find it helps to think of splitting the party the same way I think about combats. And there are a few parallels to focus on:
First, make sure everyone has something that they can do. In combat, the other characters don't wait around for the fighter to battle the monster. Instead, they each have different ways of dealing with the challenge that the monster poses. The same should be true out of combat: The rogue might be sneaking into the palace dungeon at the same time that the wizard is researching those mystic runes at the library, while the cleric and the fighter stand watch outside the museum that contains the artifact.
Second, make sure to change your focus frequently. In a combat, you go around the table quickly. Each character resolves just one or two actions, and then you move on to the next. Do the same thing with a split party. As soon as the rogue sneaks past the front gate into the palace, then cut to the wizard. As soon as the wizard has found out that the runes are ancient draconic, cut to the cleric and fighter. As soon as the cleric and fighter are satisfied that the man in the blue cloak isn't a threat, switch back to the rogue.
It sounds like you were dealing with the Point-of-View switch fine, but that only the rogue was taking advantage of his screen time. If this is because there wasn't anything else that the party could do, then work on providing a broader number of ways that the characters can progress the adventure. (And remember that Red Herrings are okay, as long as they're entertaining diversions).
But if your characters sat around because that's what they wanted to do, then that's not your problem. If a character in a combat just delays every round and never takes any actions, then it's not the GM's fault if the player is getting bored. The same is true outside of combat.
Edit: I just had an Idea. Try using combat terminology. When someone says "I stay in the bar and drink", say "okay, you're delaying." before moving on to the next player. That will help the player realize that he's wasting his time and his chance to act, and that might spur him into doing something.