14-16 days in Venice, plus other nearish cities, towns.

I would go with Padova, beautiful university city (at least in the historic center) with frequent trains east to Venice, west to Vicenza and Verona, and Ferrara, Ravenna, and Bologna to the south. Even Florence is relatively close on the Freccia trains.
Definitely less costly than Venice for lodging with lots of good food options.

From Bologna it's an easy hop by train to visit ...
Ferrara / Ravenna / Parma / Modena

From Padova it's an easy hop by train to visit ...
Vicenza / Venice

From Verona it's an easy hop by train to visit ...
Mantova / Garda

So maybe ...
Bologna - 6 nights
Verona - 4 nights
Padova - 4 nights

Could you delete the first two sentences of your post so it gets right to the point of what you are looking for.

I have no idea what jazz+travels is trying to say about the first two sentences of your request as Insee no problem there.

Having spent a full month in Venice recently I can endorse the idea of staying there and venturing out on daytrips. As far as safe neighborhoods, all of Venice proper ( not Mestre) is quite safe and if I were solo I would have no hesitation in staying anywhere on the island.

In general prices diminish a bit as you get farther from San Marco but one can find exceptions everywhere. Venice is really small and walkable everywhere so I would focus more on finding a lodging situation that suits your budget and meets your needs, without worrying about the neighborhood.

I spet two weeks here last September, and it worked well for me (65 year old single male). In September 2017 the Arts Biennale will be happening in Venice, with many free venues all over the city.

https://www.airbnb.com.au/rooms/360544?eluid=2&euid=1672ad1e-e960-aa8e-b4e3-ca2d4ed33087

Thank you all. Some great, thoughtful suggestions here that have me rethinking how to divide my time and where to situate myself.
As for your editing suggestion, Jazz+Travel: Yes, I see your point. I suppose I had in mind putting the trip in context: I'm not an American crossing the pond for a once-in-a-lifetime visit to Italy, and my specific circumstances are shaping my goals and budget.

Melissa, I appreciated your putting your question in context.

I would not spend the entire time in Venezia only because it's a schlep to get to other places. I like the other ideas posted, and I would add Este as a possibility. Small walled city with lots of art and history. Ferrara and Ravenna are two of my favorite cities.

Venice is a charming place, but in addition to it not being a central location for traveling to the other places you want to go, food and lodging there are significantly more expensive. I would spend as many days in Venice as you want to see the sights there, and then move to Verona, Padua or Bologna - or some combination of those places - for the rest of your trip.

I'd split the time between Venice and Bologna.

Check out the Santa Margherita Guest House in Venice. It's basic (Ikea furniture), modern bathrooms, excellent location in the Dorsoduro.

In Bologna I stayed in an okay hotel, Nuovo Hotel del Porto. The price was budget, the room was adequate but awkward (no place to put suitcase except the floor, bathroom without shelf space and tiny shower). The location was good, about a 10 minute walk to the train station in one direction and the historic center in another, with a supermarket around the corner.

I have stayed at Nuovo Hotel del Porto, it is as Chani described. Hotel Centrale is a closer to the main street. Hotel Metropolitan is a bit more upscale.