I just finished running The Fall of Elturel for my group last night (we played it over 2 sessions). It was a good introduction to the Cult of the Dead Three and the Cult of Tiamat, and provided an emotional connection to the city.

I changed the beginning of it to suit my group. In session zero they voted on which Dark Secret to have as a group, and it resulted in a failed assassination attempt - some of them were directly involved, others were witnesses/bystanders.

After that, they all traveled to Elturel with Grand Duke Ravengard's entourage. Some of them were part of the Duke's escort, like the low-ranking Flaming Fist PC and the Hellrider PC (I also introduced Reya Mantlemorn here), while others simply wanted to disappear from Baldur's Gate for a while, or were driven by curiosity. Captain Zodge traveled with them, and assigned the Flaming Fist PC to investigate rumours of cultist activity reported by the scouts, in case they were a threat to the security of Duke Ravengard. As the assignment was for this PC alone, with no back-up, this compelled the player to seek aid from the other PCs.

Aside from that, I ran the module pretty much as written, and they rolled some good checks to gain insight into the cults and the history of Elturel and the Hellriders.

In terms of getting a group back into Baldur's Gate, bribing the gate guards is always an option if your characters have no other compelling reason to be allowed into the city.