We needed visas to enter Tanzania, and followed these instructions: http://www.tanzaniaembassy-us.org/tzevisa.html. We had to mail our passports in to get the visas, so you may want/need to allot time for that.
Rwanda doesn't require a visa for US citizens, for a stay of less than 90 days:
We got our visas in advance of the trip, just to take care of all the logistics in advance.
However, in case you're curious -- one of our travel companions was not from the US, and there was no Tanzanian embassy in the home country. So there was no choice but to get the visa once we arrived in Tanzania. The Tanzanian embassy page states: "...a person coming from a country with no access to a Tanzanian embassy or where it is reasonably distant shall be issued a visa at the entry points in Tanzania..." It was a totally seamless process to get the visa when we arrived. There was no line, and she was through in less than 10 minutes. (Basically, by the time I confirmed I had all my luggage and was ready to go, she was through the visa line!) I don't know if this is typically the case, though.
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