This repair price will vary per repair shop and the reason being because this is a soldering job. The part itself cost will cost no more the about $6-$12 but the ability to have some one desolder the old port and solder the new port on.
At my shop this wouldn’t be anymore then about 129.99 dollar repair but then again we solder things all the time. (HDMI Replacements, Charger ports for tablets, iphone IC chips, etc.)
The repair shop you went to is probably charging you for an entire new computer or new motherboard.
The link below show a similar repair to what you would have to do if you feel comfortable doing it.
[https://www.youtube.com/watch?v=P_2OREOzg68|https://www.youtube.com/watch?v=P_2OREOzg68]