Accord what? DX, SE, EX, or LX? 2 or 4 doors? 4-cylinder or V6? The correct tire depends a lot on those details.
I can tell you that your current tires are absolutely wrong no matter which model you have and possibly dangerously overloaded if you have a EX V6 Coupe.
On a V6 EX Coupe that originally had P205/60R16 91V sized tires on it with 32/32 psi inflationthe correct +2 tire size is 245/40R18 93W (or 91Y) at 33/33 psi. A tire sized 225/35R18 87W even maxed out at 42 psi would be considered badly overloaded. Alternatively you could opt for a narrower 215/45R18 XL 91W or 91Y at 38 psi front and rear. Overall diameter is the same as OEM and its narrow width might come in handy if clearance is tight. The extra profile couldn't hurt if potholes are a problem where you live but the higher inflation pressures required won't help the ride.
On a 4-cylinder SE, EX or LX 2 or 4-door that originally came with tires sized P195/65R15 89H inflated to 29/29 psi you should be using a 225/40R18 XL 92Y with inflation increased to 34 psi front and rear. This has a nearly identical overall diameter (your current tires are 0.8" too small) and requires only that 5 psi bump in air pressure to maintain the correct load carrying capacity of 1,168 pounds.
On a 6-cylinder EX sedan, or LX sedan or coupe that originally had tires sized P205/65R15 92V at 30/30 psi the correct size to use would be 235/40R18 91W or 91Y or 235/40R18 XL 95W or 95Y inflated to 32 psi front and rear. Again overall diameter is a near-perfect match unlike your current 1.3" undersized tires and load capacity is maintained without a drastic increase in inflation pressure.
If you really don't want low-profile tires the answer is smaller diameter wheels. There is no way around that.
