Here is a nice 2 bedroom, 2 bath apartment very near the Guggenheim Museum, offered by Venice Red House.
https://www.veniceredhouse.com/apartments-in-venice/kandinsky-house-apartment/
It rents for €200 a night for your dates, so it is well within your budget.
I have rented from this agency before (10 years ago as well as more recently) and find them easy to deal with (excellent English), professional, and reliable. They are Venetian and live in the city. I recommend using this company over owner-rental websites like Air BnB, VRBO, etc. An employee will meet you at the vaporetto stop and escort you to the apartment to help you get settled.
They have a liberal cancellation policy ( free up to 15 days in advance) compared to many apartments. They have many other apartments if you care to explore the website, but this one appears to meet all your criteria.