...okay, yes, technically, but tbh what I got out of Google Translate was more natural (it’s getting better all the time).

ホテルの向かいの店で見たスーツを試着したい。

^ this is a lot more casual, mind you. To match the ‘politeness’ of the original sentence, you’d want ホテルの向かいのお店で見たスーツを試着したいです. But substantially the same, no?

Breaking down the differences:

* 私は is almost always unnecessary, and the single biggest thing that Japanese learners (at least, those whose native language is English) can do to sound more native is to learn to omit it from our sentences. My first-ever Japanese teacher told us to think of 私は not as “I” but as “as for me...”; this gives you a much better sense of how awkward it is to start every sentence with. It really emphasizes that you’re the person taking the action, as opposed to someone else — which makes sense sometimes (say, if everyone had just been talking about Jill’s plans for the day, and you wanted to change the subject), but it’s not the most neutral way to state the thing, and I think it fails to really illustrate the difference between English and Japanese grammar.

* The にある here is... well, it makes the sentence sound more like it’s saying, “across from the hotel, there is a store”. You’ll hear it more when people are giving directions. That’s not what this sentence is doing, of course; the fact that the store is across from the hotel is a more incidental detail. Thus, ホテルの向かい店 is more natural.

* 着てみたい is... fine. (Literally it means “I want to try wearing/putting on <something>”.) But 試着 is a very common する verb. (試着室 is ‘fitting room’.)

Now, I don’t know, maybe the person who put this together was really trying to provide every single part of the English sentence in the Japanese counterpart. But even then I think I would have done

I want to try on a suit I saw in a shop across the street from the hotel.

（私、）ホテルの向かいの店で見たスーツを試着したい。