Do more than check your pressures, check your sidewalls! If you have any severe dry rot or chunks of rubber taken out with interior chords showing, buy some new tires! Trust me you do not want to be stranded on a flat or blowout in the middle of a storm or snap freeze either.

Not to mention tire treads it's very easy to misinterpret how much stopping power, traction and control you have especially if you aren't well educated on cars. A lot of tires will start underperforming in wet and icy conditions even with 4/32 of tread left. A lot of tire places will charge you little to nothing to get a tire evaluation.