The majority of D&D adventures pack in a fair bit of combat, but some can be converted to a less combat oriented scenario. The key is to find adventures that have significant non-combat meat to them, such as investigation. You can then strip out all the "filler" encounters, those that are either gratuitous or which don't have anything to do with the story. Next, many encounters (especially in cities) can be handled without violence. For example instead of having the NPC be so touchy he attacks and fights to the death if you look at him funny, make him a normal person who acts normally. Now he can be reasoned with.
Also, if running a game with reaction rolls and morale rules, be sure to use them. A lot of enemies aren't in the mood for a fight, or will run away after the first swat.
For old school adventures:
The Veiled Society (B6) - Mainly a murder investigation, probably the lightest combat adventure of any of the B series. There are a fair number of potential encounters, but many are avoidable with a bit of thought, stealth, or talk. The adventure features a riot scene, and a chase scene through alleys.
An example of filler combat from B6: There are kobold explorers who trap them characters and then attack while the PCs are helpless. They don't really belong in the city, they are just there to set the scene. More importantly they don't need to attack, they could just run away. You could easily make them cowardly and they would still serve their purpose. Likewise there are a couple of zombies that attack, but they could as easily just be dead bodies. Again the purpose here is to set a scene and convey information about what is going on.
The Sinister Secret of Saltmarsh (U1) - A nice investigation adventure with little combat, and a bit of a Scooby Doo vibe. There is a fleshed out town for players to engage with.
If you have Dragon #80, the "Barnacus: City in Peril" module has a nice city that will keep players busy wandering around sampling the shops and doing investigation. It also has a haunted house (this time really haunted) leading to nicely done catacombs with a few encounters. It used monsters from the Fiend Folio.
There are many free downloadable adventures that are suitable:
Adventure Anthology One (AA1): See the "Ruin of Darkfir Castle" and "The Shepherds of Pineford". Both are very short and contain only a couple of minor encounters. download
The Haunted Tower (GL0): Exploration, virtually no combat, and features a fun Candy Cane Golem that you don't fight. Good for kids! download
Many of the free one page dungeons are puzzles or roleplay type scenarios. Here are some suggestions:
Stellarium of the Vinteralf;
Dinner at the in-laws;
A Stolen Spring;
A Rough Night at the Dog & Bastard;
Tomb of Snowbite Pass;
Den of Villainy