Try this for an alarm:

Arm it and it doesn't blink, flash or alert the would-be thief.
Someone opens the door and climbs in the car
15 or so seconds later, the door locks and the top goes up followed by the windows
Alarm with siren, lights and air horns are goin off at the same time.
Maybe a smoke bomb under the car - bright orange.
I'd suggest dye packets too, but that would mess up the interior.

*THAT* will attract attention.

 

I mostly keep the top down but put the windows up. It's more psychological than practical, but most people do have a sense of "borders" and even if the top is down, it does create a "closed area". However, if somebody wants to mess with you, they will.

As far as parking in nice places, well it ain't always true. Many years ago, I went to grad school at USC and I owned a Corvette convertible. The area around USC was mostly urban ghetto. Inasmuch as the sun had baked the rear plastic window yellow, I kept the top down all summer. No one ever bothered the car. One night I go to a movie in Westwood (home of UCLA). Unlike the area around USC it was very upper middle class and affluent. I came back to my car to find every piece of chrome in the cockpit gone -- gearshit knob, windshield washer switches, lighter, etc. all ripped off.
The moral of the story -- I don't know, but assuming that your car is safer in nicer places, though apparently logical, isn't always true.