Randy,
Termini is not the "tourist area" that many people are used to when they book in Rome - perhaps that's why it has a "lesser reputation." It is a blue-collar part of town and has many different ethnic cultures clustered around the station.
I've had many friends stay there with no issues; in fact, they all liked the central location. Because of the train station, it is the MAJOR rail, bus, metro and taxi link for the city. So there is a lot of traffic in this area.
I'm not sure I would walk from Termini to "sites," rather I would take advantage of the transportation system that's so convenient for you! The busses will go almost anywhere from Termini and as noted in previous posts you can ride the metro to many sites...
If you head southwest from Termini, towards Piazza Republica, you move into the "nicer" side of the station. This is where you'll find Via Nazionale, a major shopping street... further on you'll hit the Quiranale, Piazza Barberini, the Trevi Fountain, and the Spanish Steps - each also right off the metro A line.
If yo go the other way, you can walk down Cavour all the way to the coloseum and Forum (or just take the Metro B line two stops!).
I go to the Termini area often and have NEVER had any issues. You will see gypsies - just ignore them and hang onto your money. You'll have folks suggesting you get in their cab - ignore them also and head to the official cab stand just in front of Termini. But mostly you'll see working class Italians and budget minded tourists. Note there is a small "Chinatown" around Piazza Esquino that has a great market and many, many inexpensive Chinese restaurants.
Termini is as safe as anywhere in Rome, it just may not be as pretty... good luck!
Ciao,
Ron