It seems most simply park on the U.S. side and walk or take a taxi to La Zona. The pedestrian line getting back into the States usually (but not always) involves much less time than driving back. This is what I do 99% of the time. I like the walk across the bridge and past the vendors. I mostly go during the day. I've crossed the bridge at night but only with a buddy or two. The taxis libre (the green taxis) are not as pushy as the yellow taxis but they still try to get $5 out of you. I rode with a Mexican once and the taxi driver only charged him around $3 (when it was evident that he intended to pay in pesos).
I've never had a problem when I have driven into Mexico but I only drive when I plan on going past TJ. (Calafia is simply breathtaking but has become way overdeveloped.) I've parked in TJ and never had a problem. However, I have a POS (piece o' shit) car that doubles in value whenever I fill it with gas. I've always parked on the streets.
If you do drive, chances are you will need to purchase Mexican car insurance. Virtually no U.S. car insurance policies cover Mexico (except for a very small provision which I can't recall but I do remember it was essentially useless). Insurance for the day is usually less than $15.
Now, if you want to set yourself up to be a very popular mongering buddy, plan on getting a U.S. Customs SENTRI pass for your car. You will be assured of having plenty of rounds purchased for you. With a SENTRI pass, the wait across the border is usually 10 to 15 minutes or less, very rarely more than 30 minutes.
Happy Hunting!