Sajha Mitraharu ,
I was hit by a car couple weeks ago, the insurance adjuster wanted me to go to their repair facility for the estimate and I did, I received an estimate amount which is less than what I thought to be, it is because I have been researching the price to fix such damages and are quote much higher. The cost was added for the repair + labor. And I wanted it to be replaced with a new one parts + fair labor. I am not trying to get over , only looking for a decent settlement. Any suggestions for this situation???

You can always opt out from their recommended repair center and go to the one of your choice. If the cost run over, they will directly work with insurance to approve additional cost. But I am not sure about parts, I think they will ask to use after market parts if vehicle is certain years old, i am not sure if you can opt out from aftermarket and request to use new one or not, but you can always ask them. Lot of times it depends on insurance company , these smaller cheap insurance companies are pain in as*, to deal with.

Sounds like the other party is Geico?. You can go to any repair facility you want to..what kind of a car is it? Which year?
Most dealership use oem parts. If you go to caliber collision or service king which are these insurance company's chop shop they usually use "capa certified" parts.

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.