I had a good experience with these guys on a recent trip:
http://taxisrilanka.com
I was using them for local trips around Dambulla, but the driver was great and the owner really keen to ensure everything worked well.
I assume you mean Colombo airport rather than Mattala?
We loved Galle - stayed between Galle and Unawatuna and pottered around by three-wheeler. Great start to any trip. Do allow a good 2.5-3h from Bandaranaike airport by car - even with the expressways, there is still a big gap through suburban Colombo where the two are not joined up. It's quite interesting to get a tour of the suburbs, but it can be a but trying when you're jetlagged!
Do check up on the state of Uva NP in advance if you intend to visit, as there has been discussion of closure due to drought conditions.
We had a wonderful experience in Udawalawe NP, arranged through the basic but highly recommended guesthouse we stayed at:
http://www.tripadvisor.co.uk/Hotel_R..._Province.html
We continued from there to Ella, which was a pleasant surprise - you can walk from the town right up into the plantations (and through the rather stunning looking 98 Acres resort). There and Nuwara Eliya seem to be the top spots for plantation visits - but we were more than happy with our almost accidental DIY visit in Ella.
From there, you can return to Colombo via Kandy via a rather stunning train journey (this is one of the reasons why we only used local taxi journeys rather than a car and driver).
Have a wonderful time. I cannot recommend this island highly enough.