Can't set front door - Myshuno Art Centre Penthouse

You're right, the Fountainview Penthouse doesn't seem to have a front door, or any doors that can be set as a front door. I'd suggest removing Celebrity Home, or even replacing it with Private Dwelling, to keep uninvited guests away. I don't think there's anything else you can do about it.

@Corpsette1 Unfortunately it's not possible but I do the same thing as you and lock the door leading in to the apartment. You can try giving out keys to friends, which also helps complete the City Native Aspiration. But that does mean that keyholders will visit more often and sometimes they still hover in the lobby but sometimes they use their key and walk in. You can also lead a door/corridor to a visiting area if you have the space so nobody needs to enter the inner apartment even when entertaining. I've done this on a penthouse in Uptown on the lot where the Stargazer Lounge was before I switched it to residential. I added a lobby bathroom and a party terrace so the living space is contained. I also use Private Dwelling as @Sketch793 mentions.

I stopped using the Celebrity Lot type because my Sims were embarrassed to live there and I had to get them the Shameless reward trait, but also Paparazzi wouldn't leave and it stopped the clock from going into fast forward while my Sims slept.