Wheel alignment is the first thing to try if a vehicle is not tracking straight, but there could be other factors causing the problem.

Worn tyres or unbalanced wheels, worn suspension components or play in the steering mechanism could contribute to pulling to one side, so these are things you could also look into.

Although you have used your local tyre shop for some time, it may be worth getting a second opinion. Four-wheel laser alignment is more expensive, but it could be worth this up front cost to rule out alignment before trying other potential causes.