Tampa resident for a little over a year now here, so while not an expert, I can certainly give some details about what we've learned.
Like any major city, there are definitely areas to stay away from. And like many cities, it can be a difference of one or two blocks from a nice area to an area you want to avoid completely. The Tampa area (including all of the suburbs and over into the Clearwater/St Pete area) is rather large. Obviously, where you're going to work/spend most of your time is going to factor into your decision of where to live.
We're up in Temple Terrace, which while technically it's own city, really feels like just the northeast corner of the city sprawl. Most of Temple Terrace is pretty decent. We're about a mile from USF, and on this side of campus (east), most of the area is nice. Tampa proper is full of neighborhoods. Places like Hyde Park and Bayshore are the nicest (and priciest). Just west of USF (north Tampa) is not a nice area in general (one neighborhood up there is referred to as Suitcase City). I'm not as familiar with the west side of Tampa. South Tampa is where we currently work, and it's a mix of nicer areas and not nicer areas. I forget the general rule of the borders of where to look.... I'd have to ask around again to get some details. A few people I work with live in Carrollwood (northern Tampa) and Brandon (east of Tampa) and like where they are at. I also know a few that live across they bay in St Pete - again there I'm not as familiar with the area, but do know there are some rougher spots in the downtown St Pete area. Other generally nice areas include New Tampa and Tampa Palms, on the extreme northern/northeastern edge of the city sprawl.
The nice thing about living on the east side of the city is being close to 75 and 4, which means quicker access to head to Orlando. From our door to Disney property is about an hour drive (and about 60-70 miles give or take).
We rent, so when it comes to costs with a house (such as taxes and what not) I can't really speak to.
Traffic, for us, is perhaps the biggest difference from back home. Don't know what the traffic situation is like where you are, so I can only compare it to my experiences. The main arteries (75, 275, and 4) are heavily congested each morning/afternoon during rush hour. As long as there are no accidents, they stay moving alright, but as soon as there is so much as a fender bender, it can come to a standstill. Of course, if you aren't working the typical 9-5 or have a short commute on mostly side streets, you might not have to deal with it.
Cost of living wise, for us moving from Northeast PA, most things aren't that different. Gas, groceries, utilities, etc are all around the same as we were paying back there. Again, your results may vary based on where you're coming from. (As an example, gas is around $3.50-3.60/gal this weekend in this part of Tampa).
Feel free to PM me, would be happy to discuss our experiences and give more details/ get into specifics if you'd like.
do your research well!