There is no way to download the system, but my website is set up where you can search the MLS for free. You can even save your searches and have new listings sent to you if you'd like. I'm putting my website link below. After you are on the site, just click "Search the Tucson MLS" - It's the first link on the page.
Of course if you would prefer, I can set up a search for you and send you listings myself, but from your question you seemed like more of a "Do-It-Yourselfer". Good luck in your search and let me know if there's anything else I can do for you..