Thank you guys! I will pass these suggestions on to my friend.
Put strippers in the underground lot.
I think he needs to take care of that C.H.U.D. problem before he starts inviting people into an underground parking lot.
Parking structures, even well lighted, give people a closed in effect. Often the spaces are not as large as ground level either. There are obstructions that hamper maneuvering. Getting out takes more effort. Safety is compromised in such tight situations. Security is an issue. Nobody wants to be trapped below ground with a burly stranger headed you way. Hallways and mechanisms for getting to ground level cause anxiety at least until experienced.
I think you need to create some incentive for users or first time users so they can overcome the anxiety and form positive attitudes to the spaces. Conversely, charging for ground level parking would increase the incentive for free below ground parking. Instituting such a plan with validation tokens requires more labor and access gates. Is it worth it and would you be chasing customers down the street? If people want to spend time pursuing ground level spaces, perhaps that’s just meant to be. Once they have “earned” their parking spot, maybe they will stick around and shop more.
Thinking about this, I wonder why the elevator did not have a safety system to shut off once water was flooding the shaft (since the doors are not water-tight). Esp. given that it uses electricity, a breaker would sound like an obvious idea.
Also, aren’t underground parking garages supposed to be observed with at least a camera to prevent attacks, muggings and the like? Did nobody notice that it was filling with water? Nobody hat at least the exit drive on camera and noticed that water was running down from the street?
Sounds to me not like an indictment of underground parking per se, but a fail of security and safety measures on several levels.
Outside the US, not everybody drives a SUV yet. Most people in Europe will in fact driver smaller cars than US precisely because parking space in cities is limited and we don’t drive for 6 hrs. straight.
As for the smallness, that can be remedied by re-drawing the lines to make more space. And we’ve had complaints about above-ground parking lots with far too small spaces on this board, too.
I naturally assumed that since the OP clarified that it’s well light it’s also otherwise up to date with latest plans and not an old structure from the 60s.
Newly built parking garages are wider, bigger, better lit and come with security cameras precisely to make people more comfortable and safer parking there, because there is not enough space to keep parking above-ground. So if customers have a legitimate problem (like safety or not enough space), then it’s in the business interest’s to accommodate that by changing the problems.
If the OP has an old, cramped, unsafe garage with only lighting installed, he needs to change that first.
If he has a modern garage that people still won’t use despite being roomy and having cameras, he needs to lure them down to see for themselves that it’s a good place.
Put up signs saying the underground lots are the “A” lot. The above ground parking lot you label the “C” lot. People will assume the “A” lot is better and go there.
You mean Alpha and Gamma? 
Have the valets dress as Morlocks.
I was very curious about this myself, so I of course Googled it.
The victim was Ms. Kristie Lee Tautenhahn, 42 at the time of her death. Apparently she was 3 floors down in the garage when very action filmesque the garage wall gave way releasing a tidal wave of water. Other people in the garage who were one floor above her were able to survive by running up the ramp. She ran to the elevator, which was hit with a very powerful torrent of water, and as a result was disabled. Accounts differ, but the police believe she was knocked down by this torrent and drown.
So it’s not the awful scenario of the woman riding the elevator and the doors suddenly open to a wall of water, but an engineering flaw with the garage itself.
http://www.chron.com/CDA/archives/archive.mpl?id=2001_3326466
Exactly what I was going to suggest.
You wouldn’t believe how many suggestions I’d love to make to various places, but I don’t bother because either I don’t think they care, and/or I have no idea how to contact the one person who does care about my suggestion. (And PLEASE don’t tell me that the top people always want to hear my ideas. They’re usually far too busy on other stuff.) I LOVE when they actually solicit suggestions, because then I know that my ideas will be forwarded to the proper departments.
On the other hand, this may reinforce the notion that the above-ground lot is better than the underground lot. If customers are already doing “stupid and illegal things” to park above ground, it may get worse. Unless the shop owner is prepared to reinforce it strictly (i.e. if anyone parks without paying, call the tow truck immediately) - and they could do that now.
People are funny.
I have an auto repair shop with only one entrance, a garage door that I keep closed. There’s no parking lot, just a (very) short driveway across the sidewalk and grass strip. In big, easy to read letters on the door, it says “HONK OR RING BUZZER,” with the buzzer button (pretty obvious) right by the door. I open the door with a remote when I hear the buzzer or a honk.
Now, most people do what I consider the logical thing: they either pull up to the door in their car and honk, or they walk up to the door and hit the buzzer. But some people do what strikes me as silly – they park on the street and honk from there before walking up to the door, or they drive up to the door, get out of their car, and ring the buzzer (and yes, their horns work). It’s not particularly a problem for me, and I don’t want to embarass them by asking why they did it the stupid way 
so I haven’t asked why they did that. But it illustrates, I believe, that sometimes it can be challenging to get folks to follow what seem to be simple instructions. Heck, at one place I worked there was a sign in the front office saying “RING BELL FOR SERVICE” (since we were all in the back working) and some people just would not ring that bell.
In this case, I think it might be helpful to have an ongoing customer-education campaign, with signs extolling the underground parking reinforced by telling every customer about it face-to-face: “Do you know about our underground garage? It’s nice and cool and very easy to park in. Try it next time and I think you’ll really like it.”
Without actually asking the people, two possible explanations come to my mind:
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They do not see the sign. No matter how big you make a sign, even adding flashing neon colours, some people will simply overlook it. And actually, when I’m a customer at another place I haven’t been to before, the same happens to me, too. You are looking for a white small sign, but because the sing is yellow and big, you fail to notice it.
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Different cultural context. Some people have been raised to weird polite behaviour, where you don’t bother people, no matter what. Ringing a bell to make you notice them is rude in their thinking; obviously, whatever you’re doing right now is important, and they would die of shame to assume they are more important to interrupt your work.
That doesn’t prevent them from privately thinking how bad your customer service is, that everybody is so busy that nobody notices a customer. Trying to explain" Just ring the damn bell, we can’t afford one person just to watch the counter" won’t get across the cultural gulf, I’m afraid.
Honking will disturb the neighbors. Some of us are considerate that way.