Art,
Unless you buy a package deal somewhere, most safari costs are quoted as Daily Rates and Trophy Fees.
If you are going to hunt 10 days, then multiply the Daily Rate by 10. These prices include the lodging, food, drinks (usually but check to make sure), cook, PH, skinner, staff, etc...
If you have travel days when no hunting will happen, then those days are usually counted at a discounted rate or comped.
You may have air charter costs if the hunting area is extremely far from the nearest commercial airport.
If you don't want to use your own rifle, you can rent one from the PH or outfitter at an agreed to rate.
Trophy fees are quoted, basically if you shoot you pay for it. Each species will have a different price, typically.
If someone is going with you, but not hunting, they are usually charged a reduced daily rate (they still eat, still get their laundry done, are still waited on, etc...)
So, if you are going to hunt Buffalo in an area you can drive to (the PH will pick you up from the airport) for 10 days and you want 2 buffalo:
If the Daily Rate is 1000/per hunter per day (just pulled that number out of the air check with the outfit to see what it really is), then $10,000 for the daily rate.
If each buffalo costs $2,000, then add $4,000 of trophy fees to your Daily Rate total of $10,000.
Then you shoot $2,500 worth of plainsgame (however that comes out) you are up to $16,500.
If you go someplace that the government charges a fee, or tax, you'll have to add that. Take Zim for example, they charge 2% of the Daily Rate + Trophy fees. You are up to $16,830.
Zim also charges a Visa Processing Fee of $30 USD, so $16,860.
There is usually a dip and pack fee for trophy care (I think JJ wrote how this is done previously). For an example, let's say that is $600, so you are up to $17,460. You said you didn't want to bring any home, so that cost is of no concern to you.
Basically, that is it, except for tips and airfare!
Other costs would be you buying anything you might need (clothes, boots, bug spray, toiletries, etc...
Medical Shots & prescription meds (Cipro) if you aren't up to date for those (mine were about $600 to go to Zim)
New camera? Film? Batteries?
Over the counter remedies for allergies, cough drops, cortizone, etc...
Take over some hard candy for the trackers/game scout before leaving on a long still-hunt or stalk. Take some gifts (not in place of the tips) such as knives, sharpening stones, gloves, caps, etc... These things are easy to get here in the States and are usually fairly inexpensive, while can be very hard to come by or expensive in other areas. Don't take junk for gifts, but it doesn't have to be expensive either.
If you like to drink liquor (beer and wine are usually included in the Daily Rate price but liquor typically isn't), while in the Jo'Berg airport (or other large city airport) stop by the Duty Free shops and pick up a bottle of whatever you want. A nice bottle of scotch or high quality gin makes a good gift to the PH also.