If you are willing to stay enough see this beautiful city with public transportations, then there is a must to do: to get an Istanbulkart. You may ask ‘what is it?’ The answer is ‘it is a pre-paid, easily rechargeable card which gives you opportunity to use all public transportation system with fare payment’. Sounds reasonable?
You will be able to use tram, busses, ferries (going to Asian side of the city but except the Bosphorus cruise), subway, funiculars, even cable car with it. You may also use it for multiple travelers, it is not customized and moreover it is discounted than normal tokens and tickets. Cash payment on these transport systems is not accepted anymore that is why this is a convenient way to get around.
Istanbulkart reduced fees up to five transfers within two hours to other vehicles on the transportation network. It can be bought for 6 Turkish liras from Iett counters and private vendors all around the city, easily reloaded from newsstands and small kiosks with a sign of Akbil Dolum Noktası. A bus or ferry ride would cost 2,15 Turkish liras instead of 3. So reloading of 10 liras may be a good start to get around Old City and Taksim area.