Anecdote here, as its usually much helpful in this case.
I had took uber from Airport to city when I visited Colombo. It is easy to get. You can get a sim card from airport for cheap with your passport and it will be activated immediately (In case you don't have international roaming). You can call uber afterwards. It should be way cheaper than taxis.
As per Rome2Rio you actually have quite a few options, including Uber:
depending on the airport, you could fly to the closer airport first. Probably can ignore this option.
drive (or hitch?) if renting
each with an estimate of pricing. You can choose which is best for you