From nearby the British embassy in Kathmandu north east of Thamel, the taxi to Patan was 120 rupees, 30 minutes.
For the way back to Kathmandu, I did not find any cabs as it was night and long after tourists ought to have left already. So I started walking towards Kathmandu, and within 200m, I caught a shared cab, “20 rupees for foreigners”.
The best and fastest way to get to Patan is by taxi. It wont cost no more than 80 to 100 rupees and it is pretty much straight forward with most taxis dropping you off at the citys old gates. You can arrange for return transport but due to the high volume of taxis in the area outside the main gate there is not point. Easy and accessible.
If you simply want to visit Patan, then the best way is to take a pubblic bus form Kathmandu, where you will have no difficulties to caught it.
Anyway, I won’t reccomend you to spend a compelte day to Patan, as it is enough to stay here an half a day, you could then set a day with the visit of Patan and Bhaktapur.
In that case you could, take the bus from Kathmandu to Patan and then form Patan to Bhaktaphur or take a privat care, in that case you could add some interesting place outside the touristic circuit that are on the way (for details check my other tip).
My first plan once I was in India, was to reach Nepal and relax there for a week or so.
It was a good plan, but unfortunately I got extremely sick in Varanasi and I had to stay in that amazing city four more days.
So, I got just three days left, and with that time I had to visit as more as possible.
Once you will run in the same situation, short with time, then, it might be a great idea to rent a privat car for one day, from 03.30 am to 08.30 pm.
During the day, you will be able to visit, in a quiet chilling way the most amazing, interesting and important place, and keep other two days to visit again the paklce you did like more, or simply relax one day in the monastery.
It could work like this: every GH or agancy (better the GH for the price), is able and would love to rent you a private car with driver and guide for something like 40-60USD (it depends how good you are to reduce the rate).
The easiest itinerary would be:
Monkey Temple- Bodhanath – Pashupatinath – Patan – Bhaktaphur and Nagarkot (Nagarkot only if you are going in the right season otherwise is sensless as you will never see anything).
Such itinerary will fullfilled your day but won’t be toop stressy.
In this case, you can see quiet easily all the main places and then on day two and three visit more in detail Patan, Kathmandu Valley, Kopan and some of the temple you saw in day one.
This is a very good oprtion for those that have not so many days...