There is a lot of debate but the professionals’ opinion is the wheels and tyres should be washed first, but never when still hot. This is to avoid the excessive dirt & brake dust splattering over the surrounding areas. It also allows any overspray of the harsh wheel cleaners to be washed off the bodywork after.
Your car is still looking ok but the wheels, especially the front, look terrible? That’s probably because people do not care for their wheels like they do for their paint. After washing and drying your wheels, then why not put on a coat of wax or wheel protector, this will coat the surface and make it hard for dirt and brake dust to stick to it. It will also make them quicker to clean next time!