Welcome from another Phoenician! For some odd reason there are no shops right downtown or nearby but you might check out Don's at Uptown Plaza, Cigar Warehouse around 10th Street and Camelback, and Ye Olde --- at Town and Country Village, 20th Street and Camelback.
I go to Churchills on Scottsdale Road and Cigar King which are both near my office. Churchills' main store is on 44th Street north of Camelback and they have a small place on 6th or 7th Street west of Mill Avenue in Tempe. That store is oriented to students so they don't have the higher-priced stuff there. Also check out Stogie Cutter on Guadalupe in Gilbert.
If you're ever gonna be around this area (101 and Shea vicinity) during the day and want to meet for a smoke, PM me.