Assume that you are in Istanbul, the following are recommended sights:
Note that tripod for your camera is not allowed inside Aya Sofia, the Blue Mosque and Basilica Cistern.
1. (2 hours) visit Topkapi Palace - opens 9:00 am to 5:00 pm daily, except Tuesdays.
Take the tram on Divanyolu Caddesi (Caddesi = street) towards the direction of the palace after buying the ticket at the booth next to the tram station. Get off at the stop near the palace. Walk through the entrance with a stone arch on the side of the pavement which leads to both the palace and the Archaeology Museum, then walk up the hill to the palace entrance. Ticket required.
You can visit the many buildings, rooms, gardens and terraces, as well as jewels and other treasures owned by the Ottoman sultans. From the terraces, you can see the Asian part of Istanbul from across the waters of the Golden Horn and the Mamara Sea.
The Harem has been touted as a worthwhile place to see. There is a separate charge for it. However, I did not find the visit and the time and money spent there worthwhile.
2. (2 hours) visit Aya Sofia - opens from 9:00 am to 7:00 pm everyday except Mondays.
From Topkapi Palace, walk (about 10 minutes) on the level path towards Aya Irini without having to go down the slope back to the stone arch and then up Divanyolu. Aya Sofia is just behind Aya Irini.
You should be able to appreciate the history and ambience of this wonderful building, both inside and outside, at a leisurely pace in the two hours. Spend some time admiring the design and structure of the building, as well as the mosaics on the walls. Unfortunately, the interior of the building is marred by a huge metal scaffolding which has been there for about 10 years said to allow maintenance of the ceiling, but its removal is supposedly quite costly.
(1 hour, until 2:00 pm) Have lunch in the area near Aya Sofia. There are many restaurants nearby although most are a bit touristy, but this can't be helped.
3. (1 hour) visit Basilica Cistern just opposite Aya Sofia on the other side of Divanyolu Caddesi. Opening hours 9:00 am to 5:00 pm daily (but check).
This underground structure is an extravagant water storage tank built by Emperor Justinian to provide water for Constantinople. It has 336 huge columns and two Medusa heads at the base of two columns.
4. (1 1/2 hours) visit Blue Mosque and Hippodrome - the Mosque is open all the time to visitors if it is not prayer time
The Blue Mosque is only a 5-minute walk from Aya Sofia as they face each other on the opposite ends of Sultanahmet Park. Go to the back of the Mosque which has an entrance for visitors, change your shoes into slippers (provided); for ladies, headscarves are required (also provided) and enter the Mosque. You should dress conservatively.
The exterior of the building and minarets perhaps look more refined but is certainly less imposing than the Aya Sofia. Again the interior view of the mosque is marred by metal tubes which are placed part way down the ceiling throughout in quite a disorderly fashion apparently to support the lighting.
Next to the Blue Mosque is the Hippodrome, a public arena for chariot racing and other events in Roman times. However, there is not much left there except for the Dikilitas Obelisk (taken by Constantine from Egypt), the Serpentine Column (originally from the Temple of Apollo at Delphi), and the Ormetas Column.
5. (1 1/2 hours) Grand Bazaar - opens 9:00 am (? check) to 7:00 pm, closed on Sundays.
From Divanyolu Caddesi, walk west until the street changes it name to Yeniceriler Caddesi. Instead of continuing, turn right onto Yaglikcilar Sok. into the bazaar. Wander around to look the hundreds of shops that line the alleyways inside this covered bazaar that sell jewelry, carpets, clothing, and many other things.
If you start #1 at 9:00 am and follow the pace suggested, and allowing for a one-hour lunch, you should finish #5 at about 6:00 pm, including moving between sights.
6. (4 hours) take a dinner cruise on the Bosphorus. Before you start the day, have your hotel book the cruise for you. Cruises start at around 7:30 pm or 8:00 pm. (but check).
The cruise operator will pick you up at the appointed time and place. The cruise will go up the Straits and then turn back south Along the way you will see the Dolmabache Palace built in the mid-1800 to impress foreign dignataries, pass under the Bosphorus Bridge (one of the longest single-span suspension bridges in the world) and pass by the imposing Rumelihisar Castle, which was built in the 1452 by Sultan Mehmet to block off aid to Constantinople before its downfall. At the northern end, you can have a close-up view of the buildings, houses and mansions along the shore, close enough that you may be able to see the furniture inside apartments.
Guests on the cruises will be served a mix of Turkish and western food, or other food of your choice (but order when you book your cruise). Cultural shows such as belly dancing are performed.
The above should be sufficient for one day. You will need to time your schedule as you have to walk between places. If you are short for time, you can spend less time at the Blue Mosque, as everything you can see inside the mosque is in open view from the ground level.