Learn Arabic (Modern Standard): الطعام غير لذيذ اليوم.

While ليس is often used to negate nominal sentences, غير is a handy noun that acts like the English prefixes un- or non-. Here, it directly negates the adjective لذيذ (tasty). It is much simpler to use because you do not have to conjugate it like a verb!

How does 'غير' affect the grammar of the word 'لذيذ' right after it?

The word غير actually forms a possession structure (an Idafa) with the word that follows it. Because of this rule, the adjective لذيذ is in the genitive case, meaning it would be pronounced with a double i sound (kasratayn) at the end: لذيذٍ (ladhidhin).

If 'الطعام' (the food) is definite, why does the descriptive phrase 'غير لذيذ' not have 'ال' (al-) to match it?

In an 'A is B' sentence (nominal sentence) like this one, the subject الطعام is definite, but the information part of the sentence (the predicate) is normally indefinite. The phrase غير لذيذ acts as the indefinite predicate telling us about the food, so no ال is needed.

Could I move 'اليوم' (today) to the beginning of the sentence?

Yes, Arabic is quite flexible with words that express time. You can safely say اليوم الطعام غير لذيذ and it will still mean exactly the same thing, just with a slight emphasis on the word Today.