I was just in those countries in Aug and had no problems withdrawing money from ATMs though on this trip I was crossing land borders (went from Uganda to Rwanda, then to Tanzania and onto Kenya) and only used one airport ATM at Entebbe - rest were in various towns/cities.
If crossing land borders, there are tons of folks exchanging money where you can get rid of any left over currency and get some for the next country. It is all pretty straightforward.
As said before, you should need very little spending money on the safaris since you will have most likely prepaid for most of it. You also won't have any issues using USD to pay for any incidentals such as alcoholic drinks or gift shop items.
Not widely known is that Tanzania also issues a transit visa that only costs $30 but you have to ask for it. I believe it is normally issued for 15 days but I only got it for 7 days which was sufficient for me.
You are probably already aware of this but thought I'd mention:
- you will most likely need a yellow fever cert
- invest in a good (not cheap) pair of binoculars and make sure you are comfortable with it ahead of your trip