"...but it was closed." - 'Closed' is an adjective here. The sentence means that the store wasn't open when you went there. "...but it closed." - 'Closed' is a verb in the past tense here. This describes an action ie. The store was open but then it closed. Usually you'd add more detail (ex. "I went to the grocery store, but it closed just as I got there." or "...but it closed when I was in the car park.") You would never say "It doesn't open today", because "today" and "does" conflict with each other. Actually, now that I think about it, you could say that to talk about a store opening for the first time ever, sometime in the future ( ex. "The store doesn't open today, but it opens tomorrow (or some other time)." I'm sure that's not what you meant. "...but it didn't open today." - This means exactly what it says ie. Today the store didn't open. By contrast, "The store was closed" doesn't mention whether the store was open earlier and "The store closed" means that the store did open today.

Hello Jay! Hm, I think that the first sentence you wrote is definitely acceptable. It is really casual and something I would say to my friends and vice versa. In terms of the other words you wrote after, they do not really fit the sentence well. If you wanted to say, " I went to the grocery store, but it wasn't open today," that would work well too!