You should definitely park in San Ysidro or Otay. Unless you're part of the SENTRI program, you will likely spend a minimum of 1 hr and a max of 3 hours coming back from Tijuana City. Also, the airport in TIJ is not the safest in terms of your car getting dinged by other parked cars. I've seen it happen quite a few times.
If you park in San Ysidro, you can park in front of the Plaza Las Americas. The daily rate is about $7 USD per day. There are other parking lots such as the one behind World Duty Free that is much closer to the border on the way down to Mexico but much farther on the way back.
Otay has extremely limited parking lots on the US side. There is one that has just started working that is behind the new mini mall with the 7-11. Its $10 USD a day but is quite secure and very close to the Otay pedestrian area.
Aeromexico is offering a free shuttle coupon on InterCalifornia. The bus is older but they get you from San Ysidro to TIJ gratis. Volaris, the newish LCC flying from TIJ to TLC is also offering a shuttle service from TIJ to both San Ysidro and the Santa Fe Depot in downtown San Diego. The cost is about $165 MXP or about $15 USD. You can learn a little more at
www.volaris.com.mx They also offer pretty low cost fares into TLC with a free shuttle from TLC into Santa Fe (Mexico City burb).
The taxi from San Ysidro to TIJ should be about $10 USD.