Most people traveling to Galapagos pass through Quito, and may even linger there for a day or two on the way in or out of the islands.   Like Galapagos, Quito was recognized by UNESCO as a World Heritage Site in 1978 (one of the first).    If you schedule permits it, CNH Tours highly recommends a visit.

If your travels take you through the city in early December, you may want to consider participating in the city celebration of its founding, on December 6th (but celebrations usually begin several days before).

Here's what EcuadorExplore.com has to say about the festivities:

Ecuador's capital city is in a wild, festive mood as it celebrates the Fiestas de Quito. This most exciting of Quito's festivals kicks off annually in late November with the crowning of the Reina de Quito (The Queen of Quito), and it concludes on December 6th, the anniversary of the city's founding in 1534. The Fiestas de Quito were first celebrated in 1959, when a small group of friends decided to revive some of Quito's lost traditions. Since then, Quiteños have taken to the streets every year to party in their neighborhoods and congregate in the historic center's central plaza to dance and imbibe. There are also some customs, like bullfights, cuarenta and chivas, which residents associate closely with the Fiestas de Quito.

Bullfights

A lot of the action during Fiestas de Quito revolves around the city's bullring. The Plaza de Toros hosts fights every day and up to sixty bulls are killed during the course of the festival. The bullfights can be gory affairs, but they are steeped in tradition and link Quiteños with their roots in Spain. The picadores, mounted on horseback, are the first fighters to face the bull. They use large lances to stab the bull as it charges after the horses. Next comes the banderillero, who runs up to the bull and stabs it with small, barbed sticks. Finally the matador comes out and uses his cape to force the bull into a number of close passes. As the bull's energy lags, the matador seizes the opportunity and thrusts his sword into the bull's back, piercing its heart. The crowd goes wild when a bull is killed, cheers lustily on every close pass, and break into song at various points during the fight. Most bullfights sell out, so you have to line up for tickets pretty early to join the lively, wine-swilling spectators.

Cuarenta

Cuarenta is a traditional card game in Ecuador's highlands, but it is most commonly played during the Fiestas de Quito. Whole offices will stop work early to relax with some beer and cards. The game is not complicated, but it is addictive. Players, either individually or in teams, hope to capture their opponent's cards by matching their value. Each captured card is scored as one point, and the winner is the player or team that gets to forty points.

Chivas

Even if you don't participate in the Fiestas de Quito revelry, it's hard to avoid seeing and hearing the iconic chivas. These old wooden buses, converted into mobile dancefloors, cruise around the main arteries and plazas of the city center. As the chivas arrive in nightlife hotspots, revelers pour out and begin dancing in the street. If you want to catch a ride on one of the myriad chivas, befriend a Quiteño and start asking around; you're bound to score an invite.