two days in Istanbul

Istanbul is safer than most large cities. However, if you don't know what there is to do there, I believe you would probably do better starting with a guidebook rather than with a forum. That will give you a better idea of whether you want to go there.

Here is the first official Istanbul web site,launched a year or so back-
http://howtoistanbul.com/
This will tell you all you need to know about there is to see,do and visit.
With just 2 days I would recommend staying in Sultanahmet/Gülhane area which is the ancient peninsula where such as Topkapı Palace,Blue Mosque and Hagia Sofia are located.You would have time to just cover the very basic must see's in 2 days but at least it will give you a taste and perhaps encourage you to visit Turkey for a longer visit :)

If you're flying to Istanbul direct from the USA don't plan on doing too much in those two days.(jet-lag!)

Yes I would take things slowly-
Van breakfast in Cihangir
Fish supper beside the Golden Horn
Tired or not great opportunity to enjoy an amazing city.
Istanbul Photographer John Wreford

Istanbul is safer than most U.S. cities.

I agree that the Sultanahmet area is the best place for you to stay. I also agree (unfortunately from experience) that jet lag will likely be a nasty problem if you're coming direct from the USA and only intend to stay a couple days. While it might help to adapt to India (2 1/2 or 3 1/2 hours later than Istanbul depending on daylight savings time) it may also make it even worse. I know that the worst for me is "hopping" through time zones without a chance to get adjusted and I've had some fellow travelers tell me that such has made them physically ill. You'll be very close to that magic (real terrible) 12-hour time difference between the USA and India.

Is there any way for you to add 2-3 more days for Istanbul? If so I suspect both you and your body will appreciate the true break in travel.

Thanks for all the responses! I know we will be really jet lagged once we get there! I just want to break up all the flying. I know how exhausted I get when I fly to India. I am thinking of maybe doing like 4 or 5 days in Istanbul and then heading on to Delhi. :)

That's a much better idea. A week would be even better, especially if you spend a few days of it in, eg, Selcuk. It's a lovely peaceful place and would really set yo up for all the vibrancy of India.

Thanks for the tip! I am going to check it out now. I have decided to do a full week in Istanbul on the way to Delhi. Where else do you suggest in that area?