Udaipur has more than enough means of transport, so moving around the city is not a problem at all. In Udaipur, you will not find black and yellow taxis, which are regularly visible in the metropolitan cities. If you are touring the city, you can hire taxi/cab that is available in variety, ranging from luxurious cabs to average ones. You can choose taxi as per your preference, comfort and luxury. The luxurious you opt, higher the rent you have to pay. One can take the services of Taxis/ Cabs for a day or days, for sightseeing purposes and excursions too.
The city dwellers usually rely on Tongas, Auto-rickshaws and Three-wheelers to move around the city. Tonga, being the cheapest mode to travel, is used by people to a great extent. If you are not interested in taking Tonga ride, you can opt for auto-rickshaws, which are easily available throughout the city. In this mode, you have to bargain with the auto-rickshaw driver and set the price before hand. Unmetered taxis are also available in the city, but you have to bargain really hard with their drivers.
Three-wheeler is another option to travel around the city that charge nominal fare to reach predefined destinations. These autos run on sharing basis and move from one point to another for getting more and more passengers. Udaipur also offers a reasonably good bus service and city buses are the most common means of transport used by people. These Buses charge a small amount for the service provided by them. Usually, they don't have any fixed time schedule but run on a regular basis.
To make your trip interesting, you can also enjoy bicycle ride. Udaipur is a small city and not crowded with vehicles, so one can get around the city on a bicycle. You can hire bicycles that are available all over the city. To sum up, there is no need to be bothered about transportation, since Udaipur has sufficient means of transport to assure you a relaxing trip.