Around an hour's drive northwest of Amboseli and well beyond well-trodden tourist trails, Selenkay Conservancy is an interesting alternative to staying inside the park – it's especially good for those on their second visit to Amboseli as it's part destination in its own right, and a quieter (if somewhat distant) Amboseli base. Note that you're only allowed onto the conservancy if you're staying at the one of the conservancy's two camps, and you'll need to get up really early to make it into the park by dawn.
The conservancy's wildlife includes elephants, lions, giraffes and most other Amboseli species, making for good wildlife drives, although as a general rule you'll work harder for your wildlife here than you do inside the park. On the flipside, the possibility of night drives is a big selling point. Visits to local Maasai villages are also an important part of the experience.