The CDC recommends all the usual "routine" vaccinations (the one you got as a kid), plus HepA, HepB, Typhoid, a Polio booster, Meningococcal (if you're going to far northern Kenya Dec to June), and Rabies
Malaria and Dengue Fever are common. Malaria in Kenya and Tanzania is resistent to the anti-malarial Chloroquine.
They are in Yellow Fever zones, and although it's not mandatory to have one to ENTER those countries, it is advisable, and if you don't you won't be allowed entry to any other country (not until they give you the shot and make you wait in detention for 6 days).
as for Visas, not usually my thing but I had a quick look for you: I don't now where your home country is, but in mine (Australia) the Kenya High Commission details its visa requirements here
And the Tanzania High Commissioner to Australia website is here:
You can get a visa on arrival, but you need to pay CASH, in a convertible currency.... which can lead to delays in processing if you have the wrong money. Best to get one before you go. about 8 years ago
Tanzania - for a British passport holder, I got my visa on arrival for $50. My Irish friend had to pay $100 for hers. We did it at the airport in Dar when we arrived. It's chaos, but there seemed to be some sort of system which worked.
For shots, we made sure all the usual ones were up to date, took malaria tablets with us and we all had yellow fever shots but were never asked to produce the certificate. about 8 years ago
Sorry, didn't answer the second part - yes you can do it ahead of time. Not sure where you are from but you should be able to download the visa forms from the Tanzanian HIgh Commission in your home country:
http://www.tanzaniaembassy-us.org/ about 8 years ago
Phil - we came from the Middle East (no YF) and had been told we had to have a YF certificate. We visited Zanzibar and Tanzania and were never asked to show it. Returned to the Middle East and not asked about it.
I have subsequently been to the US, Italy, Bali, Singapore and the UK and have not had to declare that I went to a potentially YF area or that I have the right jabs. about 8 years ago