IMO, whatever other reasons there may be, a most compelling reason for learning a language is its poetry (Robert Frost defined poetry as that which gets lost in translation), and here Sanskrit poetry is unlike anything in the world. You may like to read this collection of essays[2] that my friend wrote during his first real encounter with Sanskrit poetry.
[1]: https://youtu.be/ZoS1nA8RVko?t=740 (starts at 12:20), https://youtu.be/WwtIJ8_bQf8 (ends at 35:00).
Vidya/Shishu Mandir?
We used to have Sanskrit months and weeks when we were supposed to interact with each other pretty much entirely in Sanskrit. It had such a solid grammar and I'd say it was flexible too. I wish we were introduced to it in a flexible manner. I remember myself being able to rad Sanskrit books with relative ease. But, now? Last time I tried I couldn't. I kind of blocked this language out. I talked to couple of friends and they had similar experiences.
कुत्र = where (?)
पठसि = studying. When you want to use "studying" with "you"; with "I" it would have been "pathaami" (पठामि) iirc.
संस्कृतम् = Sanskrit
So, it should roughly read "Where are (you) studying Sanskrit?"
I'm pretty much a novice but I think you may skip the bracketed _you_ because it's idiomatic to skip it when its clear from the conjugation. E.g. (You) go and (you) find him.
Also guessing that he was using material and not learning at an institution, I should have used केन (using what) Or just asked कथा (how).
संधिम् जानासि किम्
नेदम् प्रश्नम् संधिविषये