3 nights is decent - no worries
I'm pretty sure your hotel(s) would have many of the tourist brochures offering daily (and half-daily) tours of the main attractions for around 60-70 euro per person. Depending on your location - you can quite easily walk to Grand Bazzar, the Blue Mosque and Hagia Sophia (all in the old town and close to each other) - we did that and saved a few bob initially. You absolutely MUST see those 3 even if that is all you do! Also worth seeing the Roman underground reservoirs... tehy only take 30 minutes to see, but really cool considering their age... they were canny builders the Romans
r.e. Grand Bazaar - pay attention which entrance you come in from since you'd 99.9% get lost and might struggle to find your way out while the signs mostly show entrance 'numbers'. And remember - you HAVE to bargain. We managed to squeeze some great deals. Keep small change (10 and 20 lira notes) and offer them cash in hand as your final price - i.e. I bought a Galtasaray shirt as a souvenir which was initially priced at 50 and I got for 20. This is about right... their opening price is about 70% over what you should end up paying.
Hagia Sophia is closed on Mondays, iirc so plan accordingly - quite possibly one of the single greatest European landmarks of the middle ages. The Blue Mosque (built over 1000 years later) is just as impressive. Worth seeing the museum there too... there are lots of mosaics uncovered from the Roman palace that the blue mosque was built on top of... not expensive to get in, and worth a look
In close proxsimity (also walking distance, depending on your willingess to do so, of course) is the famous Spice Market which recently got an 'upgrade' for the new Bond flick, iirc. Directly across from that over the bridge you would see Galata tower (can't miss it) which is worth a visit, especially for the view. Both are worth it if time allows
Spice market is worth finding... they have lots of spice mixes to make marinades from and to put on meat prior to the barbecue... just finished my last pot, and wish we had bought more. Cheapest turkish delight was in the Spice market too... and saffron is an absolute bargain (so my Mrs tells me) The Galata tower is a good landmark, there are lots of good bars (serving alcohol and live music) around that area.
We also walked the old walls from one side of the penisular to the other, which takes about 3 hours but is a great walk.
However - if you want to go further - I'd recommend Top Kapi palace and even a Bosphorus boat tour (evening if possible, stunning views) - those are definitely worth paying for (again, around 50-60 Euros depending on length, etc.). Some even offer tours to Galatasaray and other areas.
Amazing place with so much to see and do - try and explore (as much as you can) the old part - immensly rich urban fabric and historical presence. Hundreds of little restaurants and eating spots offering good deals - you don't need to go fancy at all.
Just one piece of advice - many places do not serve alochol (Muslim country after all) so before you sit down and order food, make sure they offer beers at least. Did that mistake twice which was rather bland - the 'owners' are quick to convince you they 'do' up until the point your food is ordered (knowing you can't/won't leave now) and only then give you the good news. And do try those mussels from the street vendors - it's worth it!
Enjoy the cake / desert shops in particluar - the variety and quality of 'sweet' offerings is mind blowing and quite affordable. Yep, sweets a great. The last recommendation is to go down to the old bridge (not far from the spice market) and have barbecued fish in a baguette at lunchtime. Dirt cheap, tasty, and traditional. They are cooked and served off the back of boats moored by the bridge.. really good lunch.
You'd love it
