I am researching flight school because I am very interested in getting my PPL. I live in DFW I just graduated from college and money is tight. So I am saving money to get the PPL. I know the bulk of the cost is paying someone to train me. My question in regarding the privileges you have as a student pilot.
No, the airports you can fly from/to must be specifically endorsed by your instructor. Once you have your PPL, you can fly to any airport.
In addition to the student solo endorsement limiting you to a specific airport (or set of airports), a different flight school or flying club won't let you rent their planes unless you've been checked out by one of their CFIs. That new CFI will need several hours to check your skills, knowledge, mental state, etc. for themselves before they give you another solo endorsement (and as a byproduct, permission to rent their planes). It's not quite starting over from scratch, but the additional hours involved can easily negate a small per-hour savings. If you're even considering that a possibility, then do the research now and just start at the cheaper place, because you're pretty much stuck where you are from the time you solo until your checkride.