One thing you have to do is go to Don & Charlie's in Scottsdale.
The walls are covered from floor to ceiling in sports memorabilia. You could spend an hour walking through there looking at everything.
My grandfather played/managed back in the 50s/60s and he would always stop in at Don & Charlies even long after his playing days. We went last year, but couldn't find his autographed picture.
Another one that is no longer there was the Pink Pony. It had a lot of nostalgia behind it, but it has since closed down.
We have been to Spring Training 4 out of the last 5 years and will probably be going back.
I spend the mornings golfing and the afternoons watching baseball..
Nothing beats Phoenix weather in March.
One thing to note is that some of the parks can be spread out. If you are a Rangers fan for instance, I would recommend finding something in the NW Phoenix Metro. It can be tough to get out to Surprise.
For most of the others, being in and around the Scottsdale area would be fine.