That would be the western-style inn that my grandfather took me to in Hakone.

When you're going to or are taken to a place, make sure not to forget the "to"!

The scenery was beautiful, the hot-spring bath was heavenly, and the food was delicious.

Use "the" throughout your list to keep it balanced. Omitting 'the' could be fine in casual speech, like if someone asks how the restaurant is and you reply, "Food was delicious!" It's fine. In casual speech, sometimes people omit the first word if it's not important. In writing, though, stick to the grammar rules.

Another example of this omission being fine in casual speech is if someone asks, "What are you doing?" you reply "Going to work" or "studying" omitting "I'm" in the beginning. So this leaving out "the" would be fine in casual speech, not writing!

We often used to stay there often.

Nothing grammatically wrong in the first sentence; it sounds a little more old-school, while "We used to stay there often" sounds more natural.

My grandfather passed away years ago, but it’our trip is still mya sweet memoriesy.

I'm not sure what you wanted to say here, but this is my best guess. Using "it" here doesn't work because we don't know what "it" is referring to. If you want to say that a trip or event is something you will remember, you should say "in my memories", the in makes it grammatically correct. Saying "it's still in my sweet memories" sounds like you're calling all your memories in general sweet, which I don't think is what you're trying to say.

That would be the western-style inn that my grandfather took me to in Hakone.

The scenery was beautiful, the hot-spring bath was heavenly, and the food was delicious.

My grandfather passed away years ago, but it’s still my sweetthose are still precious memories for me.

Since you're talking about memories in the plural, instead of "it is" you should use "those are". Instead of "my sweet memories", something like "precious memories to me" or "precious memories for me" would probably be most natural.