Due to it's height and proximity to the equator, Mount Kenya has become a go-to in regards to African space elevators, but I'm wondering if another location within the Aberdare Range would be more accessible option. What do you all think?
Mount Kingangop is much closer to Nairobi, and if you did the bulk of the construction on the west side of the mountain, it would also be much easier to minimize the ecological impact, since the eastern side of the Aberdares is all rainforest and generates a lot of Kenya's ecotourism. That's unlikely to stop being a Big Deal to Kenya even in a future setting. Both mountains are as close to being 'right on the equator' as you could want realistically.
Something you'd want to think about in either case is that this is not a tectonically stable part of the world. The Aberdares are part of the Great Rift Valley and Mt Kenya is an extinct volcano. Earthquakes are a hazard in either case.
Another issue of concern is that Mount Kenya provides most of the country's water, so massive construction in that area would have some potential concerns there as well.
Honestly, considering that the elevator already is just under 36 000 km long, the few extra kilometers you save by building on top of a mountain doesn't really matter one way or another. So I would advise anchoring it wherever it's easiest to build the ground infrastructure and best transport links to the base of the elevator. Neither of which are likely to be the case in the mountain ranges at all.
The elevator is nothing like a freestanding tower, it's a hanging structure that hangs from the geostationary orbit downwards. The anchor point on the ground does not take up any significant structural load off the elevator, so the question you're asking really is just whether you dangle down a 35,786 km elevator cable/structure (down to sea level) or a 35,781 km elevator cable/structure (down to Mt Kenya). The difference in engineering effort between those two scenarios for the elevator itself is practically a rounding error.