Made it! Yes...it is possible to stay here 3 nights and it's OK! :)
Just completed my 3-night stay while attending a conference nearby. It started out pretty decent, and finished with a pleasant conclusion. The middle...nothing that I couldn't live through.
As several have mentioned already, this "motel/hotel" is extremely well situated to the famed, historical Gaslamp District. However, being that close and being downtown, you will be exposed to plenty - and I mean PLENTY - of homeless, even less-than-desirable locals. It's a fact of life in a big city - but perhaps that would be the deciding point of whether you stay at this location with children. 
Yes, the CI is old - obviously old - but they are doing what they can to maintain and upgrade. You could hear it start early in the morning, and last most of the day. You best look elsewhere if you're going to be concerned about dusty/musty corners of bathtubs where they meet the bathroom walls; you best look elsewhere if you're concerned about window-installed air-conditioners; you best look elsewhere if you're not pleased about the awkward setup of the "sink" being literally beside the beds, completely off-situated from the bathroom. 
You DEFINITELY can stay here if you're open-minded, willing to accept age and not-so Pot Purri smelling carpets, noisey ceiling fans, noisey air-conditions (but at least they WORK!), and the occassional less-than-chi-chi local hanging around the front. Keep to yourself, do your thing, enjoy the Gaslamp, a ballgame (within minutes of walking out the front door I might add), catch a movie (literally feet out to the west of the front door), or hit Buca for a fat, sodium and CARBO-infused fill-your-face-a-thon right next door. 
Dorine was really pleasant, as were the rest of the front desk staff. Soda machines on 1st (didn't work) and 4th floors (bill slot was jammed/coin slot worked). Just be forwarned...the "20oz bottle" appearing on the front of the machine is NOT what you're paying $1.50 for! :) Snack machine on 3rd, ice on 2nd... Breakfast is ok - I mean, for what you're paying and what's available at other "motels/hotels" in the area, it's probably about as good-as-it-gets (bagged eggs - warmed-up; sausage links, bagels, english muffins, peanut butter, cream cheese, yogurts, 5 cereal dispensers, waffle-maker, and so on.
Finally...upon checkout (contrary to what is currently advertised on their website), I was provided a taxi voucher to get me back to the airport. Nice touch... free round-trip I guess you could say. Oh, and speaking of out-dated website....there isn't any popcorn... :( But you can pick-up a box of microwave popcorn at nearby convenience stores.
I can't say I didn't survive the stay. Will I bring my wife and 11-year-old daughter to my next visit in San Diego...ummm...no, not at all. But if I have to come for business or a conference again? Heck ya! I'm good with it...and even ventured out on my own at most normal hours of the day and night with narry a problem. Lots of Law Enforcement and even Private Security folks on bikes to ensure the Tourist Trap keeps'em comin' back!
Bon Voyage!