Translation:I am standing at the hospital entrance.
I think it's で instead of に because the verb is taking place in that location rather than ending up in that location, if that makes sense.
You would use に if you were to walk, run, drive, swim, fly, dance, etc. TO the entrance, but で to do any of those things AT the entrance.
In English, "in the entrance" would probably mean that you were blocking the door/entrance that other people would like to use.
"inside the entrance" would mean that you had passed through the door and were inside the building.
"outside the entrance" would mean you were near the entrance but not inside the building yet.
"At the entrance" is non-specific without further information.
まちます is the action of standing up, the moment it occurs and could be translated into "I stand up". まっています describes the lasting state achieved by performing the action and therefore translates as "I am standing". Verbs that describe actions that are considered instantaneous follow that rule when using -ている.