As far as I know, you will need to get a Kenya Visa. Yes, you can get it at the border (it should be about $50). However, for as long as you remain within the EAC, you will not need to get a new visa to Uganda - if you intend to return.
So if you are going into Kenya you need a Kenya Visa, depending on which country you are from the prices may reflect it. Im Canadian and it is $50USD and cash only and sold at the Malaba border crossing into Kenya. Perhaps also at the other crossing but I didn't go that way so not too sure.
The land crossing is fairly straight forward...I did it on my own from Uganda to Kenya. I just took a matatu to Malaba, then a boda-boda 1km to the Uganda immigration to get my EXIT stamp. Then walk 200m to the Kenya immigration. Pay for your visa and get your ENTRY stamp. Once on the Kenyan side there are some shops to eat at and some Matatu's and buses.
The single entry Kenyan Visa allows you to enter Kenya, then visit both Uganda and Tanzania and return again to Kenya without paying for another visa. If you however ventured into Rwanda or DRC, then you must pay for another visa to reenter...they look closely at your stamps at immigration.
Best of luck!
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