Yes, Jandi. All the variants you've shown make perfect sense.

The meaning of "at" includes the meaning of "on" or "in" in many contexts. "at" is more general; "on" and "in" are more specific.

You can be at the beach without being on the beach.
You can be at the hospital without being in the hospital.

You cannot be on the beach without being at the beach.
You cannot be in the hospital without being at the hospital.

"at" indicates "in the general vicinity of".

So in most cases if you are in the general vicinity of some place, you are at that place.

For example, if you drive into the parking lot adjacent to the beach, you are sitting in your car at the beach. If you call someone on your cell phone at that moment, you can say, "I'm at the beach". However, you are not on the beach until you are physically in contact with the beach, walking on the sand, for example, or lying on it.

Likewise, if you drive into the parking lot adjacent to the hospital, you are sitting in your car at the hospital. If you call someone on your cell phone at that moment, you can say, "I'm at the hospital". But you can't say "I'm in the hospital" until you are physically located in the interior of the hospital building, with a ceiling / roof over your head.

Once you have arrived in the general vicinity of the beach (or hospital, or whatever), you are at that place, not necessarily on it or in it yet.

CJ