- Live for the moment
- Live for today
- Live for now
- Live for the here and now
All of these idioms mean roughly the same thing, and I think the single-word you are looking for is mindfulness.
"Mindfulness" is defined as "a mental state achieved by focusing one's awareness on the present moment, while calmly acknowledging and accepting one's feelings, thoughts, and bodily sensations, used as a therapeutic technique".
Also note this recent article from Psychology Today which says "Living in the moment—also called mindfulness—is a state of active, open, intentional attention on the present."
Alternatively, but a little more highbrow, you might consider:
"Epicureanism" - a Greek philosophy from around 307BCE. I'm sure there was a lot more to the philosophy, but today it is most widely known in pop culture for the saying "eat, drink and be merry for tomorrow we may die".