I've had a couple of spots removed with a laser. It's safe and effective. The laser hitting your skin feels like being snapped by a rubber band. It leaves a bruise that scabs over and takes a couple of weeks to heal. When the scab is gone, the spot is gone. The topical treatments that are actually effective (hydroquinone and kojic acid) aren't as effective as a laser, they take longer to work, have the potential for nasty side effects and they're not cheap.
I've always had it done a dermatologist's office. My dermatologist doesn't offer these treatments at her office so she refers patients to another dermatologist who does. I always have to go first for a consult but the cost of the consult is deducted from the cost of the laser treatment. (Obviously, this is considered cosmetic so it's not covered by insurance.) If you're concerned about sensitivity or safety issues, you could discuss this at the consult. If you decided against the laser treatment, you'd still have to pay for the consult but I think you'd find that the procedure is safe and that having sensitive skin isn't an issue.
I think some salons offer these services but I'd recommend going to a doctor. Different types of spots require different types of lasers and it's reassuring to have the treatment performed by a doctor in the event of any problems.
In summary, I give laser treatments a big thumbs up. It's quick, safe, relatively painless and effective.