How long are you staying?

oops, sorry...6 days.

April is not usually the "cruelest month" in Istanbul. We will have tulips and the promise of a great Summer in the air. The crowds of tourists will not have descended.

1. "The Other Tour" may not be as exciting for someone in your age group. For meeting locals, visiting some cafes and clubs on the Bosphorus or other in-places near Pera Palas hotel will give you a better introduction to modern Istanbul life which you can compare to the history and the historic areas as well as the suppressed subjects of the 'Turkish Empire' whom you will see on the streets between the Grand Bazaar and the Spice Bazaar, or domiciled in the area around the Chora church of the famous frescos and mosaics.

So go to "Anjelique" at Ortakoy, "Aperitivo" at Tepebasi for a drink, hit Babylon, Ghetto and/or Nardis for some live music.

2. The mineral and/or hotsprings around Istanbul are not necessarily too far away but unfortunately they are almost totally controled , managed and frequented by, at best, consrvative moslems, at worst, fundamentalists. So, I strongly recommend against them. However, you can try gender-segregated Turkish baths, especially on an evening when you're rather tired, where you can get a good scrub (if you wish to shed your skin) and possibly a so-so massage. A reasonably authentic and non-touristy one will be the "Galatasaray Hamami" just off Istiklal Street.

Consider Iznik (Nicea) for a day tour. This is a very Turkish, very local small town with a two thousand year history. If you go on a Wednesday, you can also walk around in the streets where the weekly market is set up. It can be done on a longish day and the trip will give you an idea of how the common folk travel in Turkey.
http://www.fodors.com/community/europe/daytrip-from-istanbul-iznik-nicea.cfm?8

Check Ferry schedules from Yenikapi to Yalova at ido.com

and when you land ask for the dolmoosh, a mini or micro bus to Iznik. A rental car would also be a good idea but very expensive because of the ferry cost.

3. There is the standard municipality Bosphorus tour which takes a large portion of your time. There are shorter more frequent cruises with smaller boats by Turyol and then there are others leaving Uskudar or Ortakoy lasting only one hour.

You can also take a commuter ferry from Eminonu, up the Bosphorus, very cheaply, with people going back home and at a time when photographic opportunities will be excellent in April (around 6PM)

Or, if you get up the Bosphorus some ways to places like Bebek, you can take a criss-cross ring boat which runs between piers on both sides and is rather fun.

This is the Winter and Spring schedule:
http://www.sehirhatlari.com.tr/Images/kategori/kategori/338_shkis11-1.pdf

If you will stay in Istanbul for entire time period, you can make day trips to Edirne or Sile. Sile is part of Istanbul. Seaside. peaceful. Edirne: Selimiye Mosque. About thermal spa the closest one is in Yalova. Yalova Thermal Hotel also can be option. Or Bursa day trip. There are also thermal spa hotels there. I definitely recommend you istanbul turkish baths. You can check with this link.
http://www.hamamsinistanbul.com

Very helpful information!! I just think I need to have some plans before my friend drags me to museum after museum for the entire week.
How do we get from the Airport to Istanbul? We are staying fairly close to the Grand Bazaar, I believe.

Get the Rick Steves book on Istanbul. I thought that it was very good in suggesting different tours of Istanbul.

Transportation options and costs vary according to which airport.

jumping in here with a question-- i am planning a trip to turkey for spring. we love thermal waters and were planning on going to yalova for several days-- to a thermal hotel there.

otherchelebi -- you said, "unfortunately they are almost totally controled , managed and frequented by, at best, consrvative moslems, at worst, fundamentalists" . are you saying that two american non-muslims would not be comfortable there??