gerunds - "prefer ~ing" / "prefer to infinitive"

I know I can use "prefer to infinitive" and "prefer ~ing".

And when I use "prefer ~ing", we use "to" to compare.

1. I prefer studying at a coffee shop to studying in the library.

Then, how about "prefer to infinitive"?

2. I prefer to study at a coffee shop to to study in the library.

I think it sounds not correct. rather I would use like this:

I prefer to study at a coffee shop rather than studying in the library.

Is there any other option for this? Or, is my suggestion the best choice?

Answer

Your intuition is right - "prefer to study at X to to study at Y" is no good.

Your suggestion isn't bad, but it does sound a bit unnatural. "prefer ... rather than" is sort of strange considering that "rather" itself often means "prefer".

I'd rather study in a coffee shop than study in the library.

This usually expresses a preference for a specific event though rather than your general preferences. For alternatives so you can use the infinitive in the first clause and keep the expression general, use direct expressions of comparison (all of which work with both the infinitive and the gerund):

I prefer to study/studying at a coffee shop as opposed to studying in the library.

I prefer to study/studying at a coffee shop compared with/to studying in the library.

I prefer to study/studying at a coffee shop versus studying in the library. (uncommon in writing; fairly common in speech)