The earliest evidence for celebration of the Lord's Supper comes from Paul's first letter to the Corinthians. It is clear that the Eucharist celebration takes place in the context of a meal.
The meal was likely celebrated in the dining room of a private home. Disciples of Christ Minister and New Testament scholar Dennis Smith believes that the Christian meal followed the pattern of the Greek/Roman banquet. Such a meal had two courses:
1. the deipnon - the meal itself
2. the symposium - an extended wine drinking session accompanied by entertainment
One of the many problems at Corinth was centered around this gathering. Hear Paul's rebuke to the Corinthian community: "When you come together, it is not really to eat the Lord's Supper. For when the time comes to eat, each of you goes ahead with your own supper, and one goes hungry and another becomes drunk" (1 Corinthians 11:21)
For a look at more details around the banquet, see Smith's book From Symposium to Eucharist. You can preview the section on Corinth at Google books.