Elementary positions are probably the hardest to get in this area. Are you bilingual by any chance? If so, that could increase your chances (so could Special Ed certification). Is your Elementary Ed. just up to 4th grade or does it go up to 8th? (Different programs handle Elementary differently, so just thought I would ask.) If you can add Middle School Ed. to your degree, or if it already covers middle school, that wouldn't hurt. As in many areas of the country, high school math and science are quite high in demand, so if you are interested in that...
However, if you are willing to cast your net very widely and apply to ALL of the districts in the city (including those perceived by some as "less desirable," such as Edgewood or SAISD), you will increase your chances for getting hired for an elementary position. I moved here from out of state, so had just my one year certificate, and was interviewed via phone and hired before moving here. I am currently teaching in Edgewood. I love the kids (well, most of them!) and never feel unsafe driving to/from school or walking to my car after school (on most evenings, I leave between 5 and 6 PM, so after dark during the winter). There are certainly pros and cons to teaching there, but it is a place for you to get your foot in the door for a couple of years if you think you may want to try a different district later on... or a place you may end up staying despite various obstacles because you feel that is where the kids need you to be.
Starting teacher salaries in this area are generally around the mid-40s for public school and mid- to upper- 30s for most charter schools (although those salaries can vary quite a bit; for example, I believe KIPP pays on par with or above what either NISD or NEISD pays).
Most districts here accept/require applications to be completed online, so when you guys get ready to move here you will want to start getting those filled out to get your name added to the applicant pool.