When in Mombasa try to take the local taxis, they don't look like much but they all look the same. Do not expect an up-to-date car  - you will be disappointed.  Haggle with them over the price, and you can get some good deals, especially if you stick with the same driver and they are mostly reliable to turn up to pick you up. Renting a car is not recommended-- the roads are treacherous and so is the driving. Try a tuk tuk (only for short journeys).  They are fun, cheap, and worth the experience.  Expect to get bumped around--it is all part of Kenya, so enjoy it.

When you hire a small car the prices start  around US $40 for self-drive.  It's advisable to hire a driver, which will cost you around US $15 per day. The good thing is that in case of accidents the driver is responsible, not you, although in Kenya normally in case of accident or theft the first 10 % of the value of the Vehicle is payable by the person who hired the car. The cars can take you around Mombasa, up to Malindi or Ukunda and also within Nairobi. Please be aware the car hire companies normally do not allow their cars on safari. Make sure you advise the company and they give you in writing authority to go with the car on safari. 

For Safari the right car is the Toyota Landcruiser or a comparable vehicle.  The Suzuki or Toyota Rav 4 are not really built for safari in Kenya.

For the Tuk Tuk, the cost within Mombasa business district is Kes. 50 for a maximum of 3 passengers. For longer distance the price should run about Kes. 100.  Make sure before you start with the driver that you know how much he is going to charge you.