Taking a cab to the border is very expensive and not necessary. Instead, ask the folks at the airport where to get the downtown bus to the trolley. (The bus stop is right outside the airport on Harbor Drive, the road that the airport is on.) You could actually walk to the trolley. It's only about a 20-minute walk and very nice as you walk along the San Diego Bay. The trolley takes you directly to the border crossing. (Take the trolley that says "San Ysidro".) If you take the bus to the trolley, ask for the $5 all day pass which is good for the bus and trolley for the entire day. If you walk to the trolley, it's only $2.50 to the border.
As long as you stay in the tourist areas, you will not have any problems.
Personally, unless you have business in San Diego or want to visit places in San Diego, I would stay in TJ for the two days. You can get a very nice room for much less than what you would pay in San Diego. But as some others have pointed out, if you believe you will be "chica'd out" within 5 or 6 hours, you might not enjoy bombing around the tourist areas of TJ for the rest of your time. You could hop on a bus to Rosarito or Puerto Nuevo or Ensenada but there is no mongering there to speak of unless you are fluent in Spanish. The Baja coast is something to see, though.
You may want to consider a "Toda La Noche" with a chica offered through one of the reputable agencies. It is a very different experience than the Adult Disneyland experience of picking out 4 to 6 to 12 BGs and SGs during a 12- to 24- to 48-hour marathon. Either Sampson (mexicolindobar.com) or NOB (cumintj.com) or Tania (hottijuana.net) or the folks at LatinLiveAngels.com or adultbaja.com can help you out. The agency will recommend a good reasonably-priced hotel. You meet the chica and take a cab to the hotel (or they will hire a driver for you).
Enjoy your adventure in TJ and tell us how it all turned out, okay?