Maintenance tips for MPG? (new prius owner)

Hello, just got my first ever prius, a certified pre-owned 2012 Prius V Five with 54k miles. Seems just in the first few days of driving like it's averaging around 30-35 mpg (according to dashboard) in a mix of driving condtions around the LA area; short trips, long trips, uphill, downhill, highway, city, etc. I know this is hardly scientific data, and I know I can try to adjust my driving habits to benefit my mileage, but just wondering if there are any quick things I can check with a new (to me) car to ensure I'm giving myself the best shot. I'm coming from a 2008 CR-V where I'd been averaging around 20 MPG driving from Glendale to downtown LA every day, so either way it's an improvement.

I've seen some things about tire pressure so that's the first thing I'll check, tinkering with different psi depending on tires/roads/etc. Anything else to check on maintenance/wise that the dealer may have missed?

 

Thanks for the tips so far!
I've definitely noticed the best mileage when cruising around 45 mph, maybe about 50 mpg, but that's a rare occurance 'round here unfortunately. Is there a way to check the battery health, other than with a bluetooth computer interface? Been meaning to get one of those anyway. Or taking it to a shop I guess, which I want to do anyway just to get a third-party inspection to see if anyone missed anything. Regarding air filters, is there one you mean other than the cabin air filter, the one in the glove compartment? Already checked that and it was clean.

 

So my car has a set of Cinturato P7 all season plus Eco Impact on it, but I checked them and they were only filled to around 28 front/30 rear, which is even below the door panel recommendation (33/32 or something if I remember correctly?). So I filled em up around 42/40 (though I need to get a digital guage to be more precise), and after one drive to work today, seems very promising.....although I took a slightly different route than yesterday due to traffic, I got 46 mpg coming here instead of the 34 or 35 I got yesterday. So hopefully that's indicative of a trend, we'll see!
Checked the engine air filter, super clean. I'll do the fuel injector cleaner too on my next tank of gas (assuming you pour it on top of a full tank?), because why not.

 

Well, one full tank of gas later (+ techron), this is what I'm seeing:
- Drove the tank down til 2 miles range remaining
- 308.5 miles driven since refill
- gas refill stopped after 9.6 gal
I'm assuming this means I used 9.6 gallons to drive the 308.5 miles, which would be 32.1 MPG, lower than the dashboard trip calculation of 33.5.
It's pretty confusing with the inaccuracy and variability of the amount of gas the tank actually holds (11.9) vs how much is left when it says empty, how full it actually is when the pump stops, etc.....
Anyway, I've been able to get much better mileage (45-50) on a couple individual city driving trips where the traffic perfectly matched maximum driving efficiency, but I think that's only happened driving from home to work, where there's also a net altitude drop of about 300 ft over 10 miles. Seems like coming home from work, driving mostly uphill, partly on the highway, pushing the engine to keep up with traffic, I get about 30 at the most.

So at this point I'm thinking the main factors are my driving habits and the overall hilly terrain. I don't drive crazy, but I also don't like to leave big gaps in front of me when cars accelerate from a stop, which is about a million times per drive, so I spend a lot of time with the meter in the "power" range.