I just installed hitch and wiring on my (new to me) 2012 Venza AWD. While a lot of posters bought Curt hitches, I'd read some reviews that there have (or had) been some fitting problems with Curt (pushing against bottom of bumper), and poor shipment packing. I went with a Draw-Tite from AutoAnything- good price, came in 2 days, entirely enclosed in large carton- no damage, and perfect fit.
A couple of wiring tips I haven't yet seen. There are a couple of 1" threaded standoffs poking up from the frame- that hold down the jack tray. They're painted, I scrapes away the paint at the base of the rear one, put on the ground ring terminal and a flat washer. Even with the plastic screw that holds the tray down, I have a great ground, and it beats finding a spot to drill for a self tapping screw.
Second, I ended up running the power wire beneath the car, running along the brake lines. There's a 1" or so rubber plug in the well beneath the jack tray. It pops out easily, so I was able to drill a hole just big enough for a snug fit for the wire, and thread it next to (not beneath!) the car. When all the wire was threaded, it was a snap to pot the plug back up into its hole. It seems a lot easier than cutting and threading through the grommet in front of and to the side of the spare tire. While the fit is snug around the wire, I just put a dab of RTV sealant around the hole.
Even if you're not towing a lot, I'd recommend going with the Class III (2" receiver) hitch. It gives you a lot more choices of attachments, and you can always add a cheap 2" to 1-1/4" adapter if you want- not so much the other way. Just my .02
BTW, we love the Venza (after just a week!). Our last vehicle purchase was a 2002 Camry- the curse of having a car that won't die, and just refuses to have problems. My, what changes have occurred in 10 years- a lot more features, obviously, but also a real jigsaw puzzle. My '02 4-cyl engine compartment is positively spacious compared to the Venza, and in running the wire to the battery, there were moments when I was even a bit nostalgic for my first car, a '61 Chevy 6 cyl. beater. You could literally climb into the engine compartment to do work!