Jambo! (swahili for hello!)
I did exactly that holiday a few years ago.
We spent 7 days on safari in Kenya and Tanzania and then went to Mombasa for 3 days and then Zanzibar for a week.
We safarid in the Serengeti and Norongoro Crater and Lake Tanganika (sp?) which was great.
As regards the beach part - we did not like Mombasa atall - full of tourists, touts, hassle from hawkers, run down, didnt feel safe at night etc. Would not go back.
In comparison Zanzibar was utterly amazing. (Note : I've heard in recent years it has gone more touristy, but was fine when we were there). We spend a few days in the east part of the island and visited Stone Town which is very interesting since there is a huge arab influence even though you are in Africa - strange to see arab-loking people speaking swahili! There is loads to see in the town (colonial buildings, slave dungeons, Freddy Mercury's birthhouse) and the beaches are wonderful. You can do trips to neighbouring islands too. Then we went to the west part of the island - feels much more remote, since the road to get there is very rutted and basic. The beaches were spectacular, with fabulous diving.
I would love to go back to Zanzibar (even though I havnt heard as positive feedback from people who have been there more recently).
One last thought - the nightlife is prob more lively in Mombasa - Zanzibar was pretty quiet on that front.
Ragazza.