Both locations are one of the top 20 metro areas in the US, so that reason alone meant they were going to get considered (MLB had at least one team in all the other top 20). More specifically, Arizona and Tampa Bay were seen as likely strong baseball markets since each of the two areas had been home to Spring Training for decades. They had cultivated local baseball fans for years, but didn't have teams of their own. Plus, each market is popular with retirees from northern cities, so it was felt they would attend games when their old home team was visiting.

This article from USA Today Baseball gives a good overview of the history of MLB expansion and the reasoning behind it: http://usatoday30.usatoday.com/sports/baseball/2011-04-07-angels-baseball-expansion_N.htm

Every major league sport saw expansion teams in the 90s. They all had the same basic reasons: grow into untapped or abandoned markets, grow attendance and TV viewers, generate rivalries (which are seen as the biggest drivers of attendance and TV), and of course make money.

Part of the reason MLB expanded twice in the 90s was to try to keep parity with the number of teams and with the same markets as other major league sports. Another reason is that it was a period of growing pressure to go into a profit sharing arrangement or have spending caps the same as other sports. It was felt a greater number of teams would spread out the effects of that if it happened, which it never did.