Front end shakes

New rims and tires doesn't mean a thing if they weren't properly balanced to begin with. And, those stick on weights fall off too. Could have just lost a weight. I would start with the wheels first regardless of their age.

It's not likely to be brakes if it does it when the brakes aren't being applied. Another trick would be to lightly apply the brakes while maintaining the speed the wobble is present. If the wobble goes away, it could be wheel bearings. If it doesn't, it's either the wheels themselves or something deeper in the suspension.