Sounds like you'll be there for about 48 hours. If you like shopping, go to Scottsdale Fashion Square. If you like culture and museums, second the Heard and Musical Instrument Museum. If you like outdoors, go to Botanical Gardens, and/or hiking at Pinnacle Peak or Pietswa Peak. I usually take out of towners to eat at Banderra's in Old Town and up to Sedona for a day trip, even if they're in town for just 2-3 days.
Would give Tempe a pass. Same for Apache trail; I'd rather go to Sedona. Baseball spring training, pitchers and catchers report but games don't start until Feb 27.
A car would make things easier. Unless you just want to lie by pool and enjoy weather, not that there's anything wrong with that!