Taxis are the most interesting form of travel within Isfahan. Relatively more inexpensive than you would expect, and with drivers who lower the fare merely out of courtesy for a foreigner (an unusual trait, considering how opportunist cabbies can be when it comes to tourists), taxis are the first choice for navigating the city when you have your own customized itinerary.
There are two major kinds of taxis in Isfahan. The regular cabs (orange/yellow and blue) work on a fare-sharing basis. That is, the driver will let a maximum of 4 passengers sit in a cab, and they all pay a similar fare. These cabs usually travel on fixed routes. They can also be instructed to go to a common point, depending on the destinations of the 4 passengers. They drop off one passenger at a time along the way (and pick up one or two as space becomes available). These kinds of cabs give you the perfect opportunity to mingle with locals and talk about anything from Iranian politics to social norms within the city to advice about the best restaurants in town.
The other taxis cost a bit more, but are still cheap, considering the ridiculously low price of petrol in the country. You have to ask whether the one you are boarding is not the regular (shared) one. If it is, you might as well suggest that you want to hire it exclusively for yourself, and the driver will quote an appropriate fare. This can be haggled over: if you do not succeed at first, pretend to walk away – the driver will usually call you back and agree to your offer of fare.
Then there are always the private cars, mostly beat-down and old-fashioned, that function as temporary taxis for locals and tourists alike. These can be found lurking nonchalantly around street corners. These are quite cheap, but might be risky as they are not officially registered as commercial vehicles. Board only when you are in a sizeable group, and are not loaded with valuables.