We are planning to spend 3 days in Istanbul in October. We understand that most of the sites are in the old city, and we currently have a hotel reservation in the new city. How long does it take to get back and forth between the old city and the new city? Is traffic a big problem? What is the best way to handle it?

Where in the "new city" are you staying?
Yes, traffic can be quite congested. Don't even think about driving yourself. Public transport is easy and cheap.

Seamus, thanks for your reply. We will be staying in Taksim at the MaramaraPera Hotel. We are NOT thinking of driving ourselves. Our concern is whether the transportation will take too long and we would be better off changing reservations to a hotel in Sultanhamet. But perhaps public transportation is an easy solution without engaging a taxi!?

Taksim is a nice place for your stay and an easy location for getting to Sultanahmet. Have your hotel point you in the direction of the funicular to get to the tram (specify that you are heading towards the tram to Sultanahmet). The funicular is a quick, one-stop trip to the tram, which will take you to the Blue Mosque, Haghia Sofia, Basilica Cisterns, Grand Bazaar, etc. You will be avoiding both vehicular and pedestrian traffic, so your trip on the funicular & tram is the easiest, fastest way to go. You will need one token for the funicular and one for the tram. You can buy each one at a window before you get on. You can also buy an Akbil and load it up with money if you will be making lots of trips. Akbils are sold at the top of Taksim, from a kiosk near all of the buses.

Etiler, your response is very helpful. What is an Akbil and how does it work? How often do you go to Istanbul? What are your thoughts on hiring a guide as opposed to walking around on our own?

etiler is right on, especially about getting the akbil.
Your hotel is in what can be described as the old section of the new city, close in and not in the outer, more recently developed areas. Debate about staying in Sultanahmet vs this side of the golden horn is sort of like Paris right bank vs. left bank - there are proponents and opponents of both. Sultanahmet tends to be rather quiet in the evenings, whereas Istiklal cadessi and Taksim are more lively (but not a zoo!)
Getting to the historical sights is quite simple, as etiler noted. The tram is easy, clean and efficient. Once in Sultanahmet the major sites are within easy walking distance of each other.

Sorry, I was typing as you posted.
The akbil is a stored fare device, sort of an Istanbul version of a London Oyster card. It eliminates worry about having change or tokens. See http://tinyurl.com/5rwqmb

As to a guide, that's a personal preference, but I did not find it necessary. A decent guide book can give practical info and historical background. The one place where it is helpful to hire a guide is at Topkapi Palace. There are usually guides right around the entrance, just find one that speaks English and join the group. They get the tickets for you and you avoid having to stand in line. Do take the optional Harem tour at Topkapi, it is well worth it.

Okay!!!! Many thanks, Seamus! It does sound like we have a good hotel rightr where we are ... no need to change. That's a relief!

Yes as everyone commnets, being at Pera area your life is easier, you can connect to old city easy and enjoy the life, restaurants at Pera area. Akbil is a system either you take a small gadget like keyhanger and top up as much as you like and saves you a bit on the fare or you buy coins called Jeton. If you are planning to use the tram service often and more than one person having akbil may be more efficient saves time etc.

Have fun in Istanbul,

Murat