Shimba Hills is 40km south of Mombasa. The majority of the roads inside the park are accessible by city car during the drier months, with only a couple of tracks designated 4WD only. During the rainy season you'll need a 4WD to enter the reserve.
Every safari company in Mombasa and Diani Beach offers trips to Shimba Hills (half-day tours per person from US$75). If you're travelling with others, renting a car in Mombasa may be the cheapest way to go.