What is the best non-addictive anti-anxiety drug?

SSRIs. Selective serotonin reuptake inhibitor antidepressants like zoloft Prozac Celexa Paxil (paroxetine) and Lexapro are amongst the best. So far no drug has been voted the "best"anti-anxiety agent.
There us no best one. There are several options and the choice depends on what kind of anxiety is being treated and what is the treatment history of each person being treated. What has been used before and what was or wasn, t successful. Some choices: serotonergic antidepressants, hydroxyzine, buspirone, inderal, (propranolol) hypnosis, desensitization training, cognitive behavioral therapy to name some.
Buspar, (buspirone) SSRI's, etc. Buspirone (buspar) anxiolytic drug, ssri and snri antidepressant/antianxiety drugs, and Gabapentin (neurontin) mood stabilizer drug have been used for general anxiety disorder. A person's primary care doctor or psychiatrist can evaluate and judge which drug (s) would work better, because different patients may respond differently to the same drug.
And... Cut down caffeine & junk food. Eat veggies, fruits. Work w/ doctor & herbalist w/ herbal remedies that may be useful: adaptagens such as ashwagandha can reduce cortisol (stress hormone) levels, schizandra. L-theanine (from tea) 200 mg when needed. Longer term (ranked from mild to strong): chamomile, lemon balm, milky oats, valerian, passionflwr, hops. Also consider inositol, vit d3, magnesium.