As far as the tire itself is concerned, you can air it to the max on the sidewall when cold. But that can be dangerous because if the car isn't heavy enough to match, it will ride mostly on the center of the tread and you'll have less traction. Choose narrower tires and air them up hard for best mileage, but realize it will compomise the handling.

Tire pressure makes a considerable difference, but driving gently, not using the A/C, and removing unnecessary weight from the car are the other main things for better mileage. Honda pretty much optimized the powertrain for mileage so modifying it isn't going to change much. The modifications on the market are all geared to higher performance anyway.

 

I would suggest using the inflation pressure listed in the door jam, that's what they are there for.

 

Those figures are only ballpark for stock tires and rims with what the mfr thinks the average driving weight of the car is going to be. 'Better way to find proper pressure for the tires and weightis to chalk the tread and drive a few feet, checking the treads for even wear. There is going to be a "range" of a few PSI that yields fairly even wear. Run a little on the high side of that range for that weight and those tires for the best balance of gas mileage and even treadwear.

Honda could also use lighter/skinnier rims and tires for better mileage, but the handling would be compromised.