1999 cherokee, Heater core has been leaking for a long time so I'm finally going to bite the bullet and pay a professional shop to do it because I just don't have the ambition to do it myself. He is replacing the core and the AC evaporator and will evacuate and recharge the AC. He quoted me a price of $675. Is this a good price?

That's a good price.

Just recharging the AC here in Oz costs $250. So, taken into account that its a shop + the labour and parts, it sounds not too bad.

In Oz?

Are you a midget? Do you know Dorothy? Do you drive on the yellow brick road?

Down Under matey.
And yes, Dorothy I know
We all, kinda...

Damn good price. I got quoted twice as much.

Beware of the huge difference in quality in heater cores. Can't tell you how many $75 heater cores I've seen that have failed prematurely.

I buy plenty of aftermarket parts, but when it comes to heater cores, because it is such a labor intensive job, I will only use and recommend Mopar cores, purchased from Jeep. Yup, they are over $300. But once you do this job, you do NOT want to do it again! Genuine MOPAR cores have been proven to stand the test of time........

X2 on Quality parts in there.
I believe that Jeep started building the XJ with the heater core suspended, and built the vehicle around it.
The Haynes manual describes the details of removing it.
As for cost, I cannot advise.

That is a fair price here in jersey. It's about a 5-7 hour job. The parts will be a couple hundred bucks.