Just got the 2017 Toyota Prius Three Touring and need some advice

Welcome to PriusChat.

The Prius, unlike many cars, gets better gas mileage in city driving. There is a large mileage penalty for short trips. The car seeks to run the engine at close to peak efficiency, so some mileage is lower while the engine is getting up to temperature. This penalty is spread out over a longer trip.
Slow braking helps reclaim the energy of motion into traction battery charge. Some people think the software is set up for "safe" settings and it learns & adapts to the particular components as it is driven.

Since you have a Generation 4 Prius, be sure to check out those forums. Although much advice will be the same across generations, the 4th is also quite different.

 

Here are a couple more suggestions.
Check your tire pressures. My dealer had the pressures much below the recommended ones. Many people find improved mileage without loss in ride comfort with higher pressures. I would not exceed the max pressure listed on the sidewalls, though.

The Prius will accelerate briskly if needed. The different drive modes (Eco, Normal, PWR) just change the amount you need to press the accelerator. The drive mode also affects the responsiveness of the Radar Cruise control. I am currently running in Normal mode and will likely transition to PWR mode to gain Radar Cruise Control responsiveness.

It is sometimes better to accelerate a little more briskly and then coast or maintain slight acceleration. I tend to use the "Hybrid System Indicator" in the middle screen (next to the speedometer) to maintain acceleration in the Eco mode when reasonable. That display can be changed by the 4 way control on the right of the steering wheel.

 

Here is a photo showing the Hybrid System Indicator, but it is from a left hand drive vehicle. Our display is to the right of the speedometer.

 

congrats and welcome!
how many tankfuls have you gone through? you need to calculate mpg's by refills at the pump, and the dealer tank does not count.

 

^ Purchased Saturday.

Yeah give it a few tanks, track your fillups and mileage, still early days.

 

Zippy accelerations will hurt your mpg. The car can be enthusiastic (for a Prius) but if you can hold back from flooring it, your MPG will improve. This is in addition to the advice above, but as time goes by you'll get to feel the rhythm of the car. Personally, I find using the Normal Mode is the most natural and rewarding experience, but there is no right or wrong choice.
Welcome to Prius Chat and enjoy your new car..