Brother, if your goal is to repair your car, then why are you disappointed with this quote? If you are quoted a price (despite it is lower than your expected price) from the insurance's recommended repair shop, then that shop is ready to fix for that price. Simply go with it and have it fixed. (Note: Generally, insurance company will reduce your deductible if you select their recommended place.)

if your goal is to get money from the insurance and fix it somewhere else, then like other people mentioned, you can go anywhere you want. Go to Yelp and search for an expensive car repair shop in your area, then have this shop send the estimate. You will get a decent settlement this way.