East Africa - Help Planning

Myself and my partner are trying to plan a trip to East Africa at relatively short notice after an opportunity came up to visit in the second half of June (13th-25th). Neither of us have been before and we're finding it difficult to figure out the best option, we haven't had much spare time to plan so we contacted a travel agent and they recommended the plan below but we're not really happy with it:

• Fly Malwai to Nairobi - spend 4 nights there - this seems way too long based on what I've read
• Safari for 3 days in Masai Mara - Lake Nakuru
• Mombasa for 3 nights - again seems quite long, particularly if we spend 4 nights in Nairobi and follow it up with 3 in Stonetown
• Zanzibar for 3 nights

The only stipulation is it has to begin in Malawi. What we'd like:

• Safari - we're happy to go wherever is best
  • Originally been thinking Tanzania but availability doesn't sound great according to the TA
  • We're aware of "Safari fatigue" so don't want too long of a stint
• Some time at the end to relax -
  • Zanzibar sounds ideal but neither of us can spend days on end on a beach either so we can't overdo it.
• Anywhere interesting to visit, has anyone been to Lake Malawi or Liwonde NP in Malawi?

We're aware it's going to be an expensive trip and while we're not loaded by any stretch we see this as something that might not come around again. If anyone has any experience or must-dos we'd appreciate it!