Terri,
I am a 25 year old female who stayed in a hotel right near the train station in Venice alone just this last September.
I whole heartedly agree with the other posters that Venice is a safe city. I enjoyed staying near the train station because I didn't have to haul my luggage onto a crowded vap! Rather, I just walked for 3 minutes down a main street to my hotel! Also, you can walk to the Rialto bridge from that area in just 10-15 minutes.
At night, the area around the train station is chock full of people, which adds to a feeling of security. Even stores are open late (until 10 or 11 pm if I remember correctly). Good luck and have fun, I'm jealous! Venice is magical.
Jenny