I would not stay in Tijuana at all. It is primarily an undesirable location, unless you are 19 and just got off three month's sea duty, that is.

Right after you cross the border you will be mobbed by taxi drivers. Select one who speaks some English, and negotiate a price to Rosarita Beach. Do not take a rental auto over, as driving in Mexico is quite adventurous.

The beach spot with the lobster tails sounds good, but, I have never been there. However, Rosarita Beach is incomparably preferable to TJ.