Here are some suggestions for day trips from Nairobi:
Nairobi National Park - close to Nairobi (within the city, actually) and you can see lots of animals. An easy half or full day. Follow the link for tour suggestions.
Amboseli National Park - this is a whole (very long) day (from 4am to 10pm). Chiara recommends this tour that she and another dada took in 2019.