Indeed, I'll agree with MSerforfun , there is nothing special about Taksim at all and although Istiklal Caddesi has a lot of culture, in my opinion, it shouldn't be a primary tourist stop since the old charm of that street has left it's place to outlet and average stores that you could find at any mall.

However, if the OP wants to stay at the Grand Hyatt, the best option would be to get a taxi from the taxi rack at the airport. If he wants a van ( per his other thread ), he could request a luxury taxi ( Mercedes Vito ) for the double price of the regular taximeter at the same location where he could request a yellow taxi. Of course, there are transfer services available but they are tourist scams thus I don't use them or recommend any but if the OP would be more comfortable booking a pre-paid service, he could certainly book one for 3-4 times of a regular taxi. Another alternative that I could suggest is to split into two yellow taxis.