Place to stay in Venice?

You should use www.booking.com to locate hotels and apartments for the dates and locations you are looking at. There are lots in your budget. The problem is that Venice is somewhat of an event/convention city and hotel rates can vary a lot depending on what is going on in town on a particular date. The map view function will show the actual location and prices.

I am also looking for lodging in Venice for next September. I emailed the place I stayed last time I was there (near Accademia vaporetto stop ) and asked about the seemingly reduced availability.
The man who answered from the front desk told me: "as usual September is a very requested period. During the first week we have the Cinema Festival and the Regata Storica on the first Sunday."

So depending on when you are looking, you might find less available than one might expect.

Good luck. And enjoy your trip.

I stayed here last October. It is by the hospital. Not real close to San Marco but not horribly far away. Massimo the owner has 2 apartments in the building. It looks to be available in September. https://www.airbnb.com/rooms/3043430

There is a huge International Film Festival in Venice each year first week or so in Sept. many Hollywood stars are in town ; later in the month will be easier and cheaper I am sure.

We stayed in the Hotel San Samuele, about a 10 minute walk to San Marco, this past September. Convenient, quiet location; about $150 per night. Would highly recommend.

closer to San Marco is not where I'd recommend. First, nothing is really far in Venice. Second, a lot of sights aren't that close to San Marco.

I always stay in the Dorsoduro - I've stayed in 3 different places, all were great locations with easy access to the vaporetto and all were no more than a 20 minute walk to San Marco and room rates are definitely lower there, plus it feels quite residential and away from the very touristy Piazza. The one I'm returning to in February is a guest house (Santa Margherita), so budget (well, for Venice, budget) prices. It's basic, with mini-fridge and electric kettle in the room and a modern bathroom/shower. There's a communal kitchen where you can make breakfast (or any other meal). By law, they can only offer sealed food, but they provide cakes, crackers, and other stuff (I don't remember from 3 years ago). I'm paying €90/night for a single during Carnevale (the highest prices of the year in Venice).