The other option is to go for a silver service cab for the run from the airport to your hotel. You book in advance, they will guarantee a child seat and will actually be there holding up a sign for you (like a limo service - so you feel very important and almost famous) and all the stuff that makes life a little more comfortable and from memory they are the same fare as a taxi but with an additional charge or about $12 but for the ease of mind well worth paying it IMHO.

Once you are at your hotel just use public transport or ask the reception to book you a cab with a baby seat and then they will make sure again that you have one.