If you've decided when you're going to Spring Training, the games you plan to watch and the parks you plan to visit, you're at the point of deciding where you plan to stay. Here are some ideas, again from a Rockies-centric point of view:
Stay somewhere in the East Valley, either Scottsdale or Tempe. If you're going to Spring Training to see the Rockies, it's best to stay in the Scottsdale or Tempe areas. Several of the Spring Training parks are within a 15-minute drive of Scottsdale, which makes for an easy drive or cab ride. There are plenty of affordable places to stay in the area, and it makes life much more convenient to be near the parks. So my advice is to not stay near the airport or west of downtown if you're going to see the Rockies.
Stay somewhere within walking distance, or a close cab ride, to the nightlife. If you're interested in taking advantages of the restaurants and bars in Scottsdale or Tempe (more on that below), consider staying as close to possible to the hubs of major activity. In Scottsdale, that tends to be Old Town. There are plenty of great places in Scottsdale, but Old Town offers the highest concentration of restaurants and bars in one area. For Tempe, Mill Avenue is the main strip for college students, so it has more of the college-type bars and nightlife. If you're angling for that, it's best to stay close by so that you're a quick walk or taxi fare home. In either location, you'll be close for driving or taxiing to games during the day.
Consider your traveling party. Scottsdale is an expensive part of the Phoenix metro, but you don't have to spend your entire budget on lodging. If Spring Training is a Guys' or Ladies' Trip and you don't mind Spartan conditions, you can find comfortable rooms in the Scottsdale or Tempe areas without breaking the bank. If you're traveling with family and looking to save on a room, broaden your hotel search to include independents as well as chains. For two of the last three years, I've stayed at a locally-owned place on McDowell Road that, while not within walking distance to a ballpark, Old Town or Tempe, was still a short cab ride away. It's been comfortable... and inexpensive.
Baseball may be in full bloom in the Cactus League, but you won't spend all of your time at the ballpark. Some games are in the evening so, unless you're going to another game during the afternoon, you'll have some free time during the day to relax or take in the sights. Of course, most games are in the afternoon, so you'll have an opportunity to explore in the evenings, as well.
During the Day:
Scottsdale has several great golf courses if you're interested in bringing your clubs, and the March weather is perfect for a round.
In addition, Papago Park in Phoenix has hiking and mountain bike trails, and even a few larger rocks to climb. Hiking up A Mountain in Tempe is also a fun way to spend a morning.
If you haven't seen Chase Field, it's definitely worth touring and makes for an interesting contrast with Coors Field. Chase Field offers tours year-round twice a day (although maybe not during the World Baseball Classic on March 8-10). The light rail, while limited, runs from Tempe to downtown, with a stop at Chase.
If Chase Field's architecture isn't sophisticated enough, head east of Scottsdale to Taliesin West, Frank Lloyd Wright's desert home and studio. Tours are offered daily and it's well worth seeing.
During the Evening:
Scottsdale and Tempe both have great restaurants and bars, and you won't run out of places to go while you're there.
As mentioned above, Mill Avenue is the main college drag in Tempe, with plenty of college bars and a few restaurants. More restaurants and bars can be found if you venture off Mill but still within easy walking distance.
Tempe also is home to Four Peaks Brewery. It's an easy cab ride from Mill Avenue, and a must-visit place for local beer and pub fare. Four Peaks has several terrific year-round beers, and its seasonal offerings are great, too.
Scottsdale doesn't cede ground to Tempe when it comes to craft beer. Papago Brewing in Scottsdale is another terrific brewery and brewpub, with plenty of handles pouring beers from Arizona and beyond.
Old Town Scottsdale is the place to visit not only for bars and nightlife, but terrific restaurants. There are multiple brunch spots in Old Town for grabbing breakfast before a ballgame, and plenty of places both plain and fancy, depending on your interests. The downside is the festoonery of orange and black for the Giants, who play at nearby Scottsdale Stadium, but you'll grow to ignore it.
Spring Training is an excellent way to spend a long weekend in March. Whether you're a hardcore fan going to scout your team and its rivals, or a casual fan looking to enjoy the sunshine while cheering on the Rockies, the Cactus League has something for everyone. Most importantly, it has baseball a full month before you can get it in Denver. That's reason enough to make the trip.
(One footnote: Other than Four Peaks and Papago, I didn't think it right to make specific recommendations in the text. If you have questions about specific places, let me know in the comments and I can try to help.)