Tampa's like my second home!  And when I travel there, I usually go on extended stays and end up working remotely from there, and thus have come to find a few cafes with wifi (they're not very prevalent there, so it's like finding buried treasure when I come across one).  Here are two of my favorites:

• Tre Amici @ The Bunker in Ybor -- indie cafe with a really cool, hip vibe.  Very chill place to hang out with good drinks, nice light bites and weekly shows and open mic nights.  Love their homemade hummus, and they also serve wine!
  
• Kaleisia Tea Lounge -- near USF campus so lots of college students.  They have an amazing selection of tea, from hot and iced, to bubble!  They also serve small vegan dishes and occasionally have little events where you can get free bubble tea.
  

Those are my two favorite indie cafes in Tampa that have free wifi.  Here are a couple of chain spots that have free wifi, too:

• Barnes and Noble -- I think there are two in Tampa.  You can grab a drink from the Starbucks inside the bookstore and just hang out with your laptop.
  
• Panera Bread -- there are five of these in Tampa and all of them have free wifi.  At any location, I'm a sucker for their baked potato soup in a bread bowl :)
  

Buddy Brew Coffee in Tampa has Wifi. It’s probably the best coffee in Tampa.

All libraries have free wifi...they are all over Tampa. Panara Bread also is a good option.  Several in Tampa.

all mcdonalds have free wi-fi.  when you set up in one you can use it at any mcdonalds