Where do you park in Venice

The best choice would be to do Venice at the beginning of your trip (before you pick up the rental car) or at the end (after you drop it off). Keeping a rental car for two days to gather dust in a car park is an expensive option.
If you absolutely must, then drive across the bridge to Piazzale Roma and there will be several huge multistory car parking structures both there and at the Tronchetto island, next to it. You can see all of them on Google maps or also on Street View. I parked there this past summer for half a day and it was a lot of money. I think you might be able to park there for a flat fee under €30 day. As far as safety they are as safe as any parking structure (like the ones at major airports) could be. The biggest risk is a ding from someone who is not careful opening their car doors, spaces can be tight.

You might consider parking at the airport and taking the shuttle bus to Piazzale Roma. It's an open lot and was 5 euro a day two years ago so may have gone up since. The bus ticket each way was another 5/6 euro and the ride takes about 20 mins.

Just checked its website - the Tronchetto parking garage is 21 Euro a day. It's very easy to drive to and there is a vaporetto stop on the ground. Park as close to the far side as you enter as you can. The elevator on that side is closest to the vaparetto.

Doug is right about the parking garage situation. Just be sure to park at the other end as that's where the vaporetto stop is.