Jibby I had this problem and had a similar quote , I found the leak by using compressed air to pressurise the system , if it's a small leak then this won't work and they have to put a dye in and charge the system to find the leak , it turned out to be in the condensor under the dash .
I found a half cut and got in and removed the condensor which gave me a heads up on how to do mine , believe me if it's under the dash then $700.00 is cheap !!
Just make sure they are good air con guys , if need be go to a place where air con stuff is all they do , taking the condensor out and replacing is a full days work .
Take in mind that after I had replaced the condensor it still cost me $300.00 to have it regassed and a new dryer fitted , so if you take that off the $700.00 it's not costing that much .
If you have no experience at this I would pay my money and smile !!
It's not rocket science [ almost !! ] but it's time consuming and tricky , you have to be so careful not to damage things like the tiny capilery tempature tube , if you are a patient practical particular kind of guy with two days to spend on it then go for it , otherwise just pay for it , it really will be money well spent .
Try and get an understanding from the people doing the work that if it turns out to be a leak not under the dash that is easy to find and fix , then the bill will be lots less ?