Know the Places to Visit
Plan which places you are looking to visit. Do some homework and see which particular historical sites interest you more than others. These places will set the tone for your tour so select them wisely.
Search for Tours
There are plenty of pre-planned tours that are available for reasonable prices and you can give them a look to see if one suits your needs or not. Ideally you can see all the places in the same trip but you may have to take more than one trip for this purpose. You can also see if there is an option of custom tours but they may be quite expensive.
You can engage cabs or use a single cab to look around and see all the historical sites of the city on your list. This way you can look at all the places that you want without any time bar or other restrictions that are associated with planned tours. Cab drivers often know each and every corner of the city and they can get you to all destinations quickly. It will obviously be a bit costly but it will be well worth the expenditure.
You can set up an adventure as well by using all modes of public transportation in the city and move around freely. This will certainly save you a lot of money and will add a lot of fun to the whole experience. You will be able to move as you please and discover a lot of new things in the process. However, if you opt for this, be ready for quite a bit of walking.