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I think the problem with the first version is that it mixes tenses rather awkwardly....
"We had a wonderful meal. The food was delicious."
Simple past tense.
"We were eating happily"
Past continuous tense.
"light music was played."
Simple past tense again.
You could say "We had a wonderful meal. The food was delicious. We ate happily while light music was played."
This keeps the whole thing in the simple past tense.
The second version mixes tenses too, but it's okay....
"We had a wonderful meal. The food was delicious. While we were eating happily, light music was played."
Placing 'while' here prepares us for the transition between tenses.
Whether you'd use the first version or the second would perhaps depend on whether the narrative goes on to describe events at the time of the meal, or after it. If you wanted to describe events at the meal, you could end the sentence with 'playing'.
Urgent 
Linear Mode
