Generally it costs around $300-$400 for the install if you already have the ring/pinion and bearing set. This would also be an ideal to rebuild the factory trac-loc unit as well.
Going from the stock 3.27 gears ( 3.23 gears aren't even available for the 8.8. inch as far as I know), to 3.73 gears won't really have much of an impact at in city/around town driving, and the hit on highway mileage won't be much, you might lose 1- 1.5 MPG on the highway, but overall it's pretty minimal.
Ring and pinion swap shouldn't cost too much, definitely no more than $500.
As for mileage, I have 3.73s in my 98 Cobra (previous owner put them in...shoulda put in 4.10s), and I will say, I do quite well on mileage. A 98 cobra was originally rated at 16/24mpg city/highway, and I average about 23mpg mixed city/highway, and I've gotten as high as 34mpg (really!) on the highway. So you shouldn't even notice a difference. Especially if you don't try to do 80+ everywhere. When I cruise at the speed limit (65-70) is when I get the best mileage. Slower or faster and it drops.
All depends on who does them. I charge 400 but i have heard some shops charging as much as 900. Call ahead and get a price first. If you were worried about gas mileage you should have kept your 3.23 in it. 3. 73 will drop your milage about mile or 2 per gallon all depending on how hard you drive.
Actually theres a website that does exactly that, you can setup a virtual car and then do any kind of mod, final drive ratio in your case, then the app computes how the car is going to change after that, try at http://www.nxgtrsim.com