Look up.
I'll try to compile the choices we've had so far...
The Village of Hommlet
The iconic town of AD&D, designed by Gary Gygax and shown in the adventure module of the same name. Hommlet is a sleepy hamlet that just happens to be near to the Temple of Elemental Evil. It saw a lot of action during the first rising of the Temple, then reverted to its sleepy state.
The second rising of the Temple is where it first was published: the nearby Moathouse is inhabited by agents of Chaos and Evil, and cultists infiltrate the village. Local retired heroes provide training for the members of the party, and there is tension between the Old (Druidical) Faith and the new faith of St Cuthbert.
The third rising of the Temple (as published in Monte Cook's
Return to the Temple of Elemental Evil) sees Hommlet no longer quite so sleepy.
Threshold
The example town in the D&D Expert Set edited by Mentzer (possibly also Moldvay; I'll check). It has a few inhabitants detailed and some adventure hooks. It is set in the Grand Duchy of Karameikos. Monkey Boy notes that it sees extra detailing in
B10 Nights Dark Terror, but I never saw much of late-Basic D&D material.
Restenford
Less well known than Hommlet,
Restenford is the town featured in the AD&D adventure "L1: The Secret of Bone Hill" by Len Lakofka. It's set on Greyhawk in the Lendore Isles.
Keep on the Borderlands
If you don't know this place - probably the most well-known of any D&D adventure, due to its including in many, many sets of Basic D&D - you should hunt down a copy. The dungeon may not always make sense, but it's designed to be fun for beginning players & DMs. In that it succeeds.
The Keep itself is unusual in that none of the NPCs are named. Another Gygax design, it has infiltrators, tavern-keepers, a head priest, and interesting places to visit.
Cheers!