Would like to stay near the train station-within 4 blocks
in a safe neighborhood under 150 euro per night and
near a vaperetto stop-any recommendations-thanks in
advance
We have stayed twice at Hotel Florida, very close to the train station (vaporetto stop is right in front of the station.) No elevator if that's an essential for you.
We are staying at B&B Allegri (Allogi ai Bareteri) http://www.bareteri.it/. and it was recommended to us by other travelers. Also suggested that a spot in between the St. Mark's and Rialto Bridge would be most convenient. Also the Duodormo area was recommended (near Guggenheim museum and more of a neighborhood with nearby university). I found great places on airbnb but ultimately because of my fellow travelers went with someone who had breakfast and closer to the sites. Good luck!
We stayed at Ca' Due Leoni. It was a relatively short walk from the train station and its vaporetto stop. It wasn't the most amazing place in the world (no character), but it works if you're on a budget and just looking for a clean place to sleep. At the time we traveled, it was the cheapest place I could find in that neighborhood that still had reasonable reviews, so that's why we picked it.
Much of the Dorsoduro is less expensive than around St. Mark's, and 5 minutes' walk to the vaporetto. I can't think of anywhere that isn't safe in Venice.
Last week I stayed at Hotel S. Lucia in Cannareggio. Less than a 5 minute walk from Ferrovia station. I paid 55 euro a night for a single room with shared bathroom (sink in room and WC right next door). They serve breakfast in the lovely garden! The staff is extremely friendly and helpful.