To my mind the best way to travel along the city is to walk. When you go on foot you do not depend on any kind of transport. You can observe the beauty of the buildings and landscapes wandering along the streets, you can go anywhere you like. These are the advantages. But of course the disadvantages of foot walks are the time you spent while walking. If you are short of time and you are in a hurry it is better take advantage of any means of public transport. If you live not far from the underground I advise you to use this means of transport.
First of all it's the fastest. Underground trains run every 3 to 5 minutes. It is also the most reliable type of transport. With trams, trolley-buses and buses, there are lots of things that may interfere with their normal operations. But all years I have been travelling by metro it has never let me down. As for the fare, it's a little more expensive than trams and trolley-buses but cheaper than most buses and shuttle minibuses (route taxis). The only problem with the underground that it does not cover the whole city. But every metro station has good trolley-bus, bus and shuttle minibus connections. You can also travel along the city by car if you have one.
But the traffic in the city is very heavy, especially during the day time. There are a lot of traffic jams on the roads, so maybe it is more convenient to go by underground. If you want to reach the place of destination without any problems and in a short period of time you can order a taxi by telephone. But bear in mind that it can be rather expensive. I wish you to have a good time and nice impressions of the city