War of the Burning Sky is no Dungeon Crawl. Indeed, it's about Chapter 6 before the first Crawl appears, IIRC.
Chapter 1, for example, takes place in a besieged city, the action starting as an aerial battle takes place overhead. The PC's first have to escape from enemy infiltrators and a burning inn (at the same time), encounter a potentially hostile spy and his LG celestial accomplice (this gave the Paladin in our group a few moments of moral dilemma), before attempting to retrieve a caseful of espied data and escape from the city under the noses of a hostile army.
Best of all,
The Scouring of Gate Pass can be downloaded free*, and includes a map and mini-gazetteer of one of the most unusual cities I've seen in 25+ years of RPG-ing.
Other Chapters include moral dilemmas, negotiations with monarchy, information-gathering and mass battles between huge armies.
Necromancer Games have two excellent products which are less Crawl than one might expect.
The Lost City of Barakus details a city, wilderness around it and a multi-level mega-dungeon. The city includes numerous opportunities for adventure, plus detailed NPC's and room to develop unique plots. The Wildeness also sees much love, multiple encounter sites (not all combat) and various plot lines. The Dungeon, even on the first level, has areas where negotiation is better than fighting and a careful approach is better than kicking in the door.
The Grey Citadel mixes combat with investigation, role-playing, mystery and intrigue. There are fights to be taken, but there are multiple ways that the adventure can be taken. When I ran it, I had two or three sessions where the majority of the time was taken up with RP and I had to chuck in a combat for the blood-thirsty members of the group.
* The 3.5E version that is. Don't ask about the 4E conversion, OK?