NAMGYAL TSEMO MONASTERY - situated near the Leh palace and an even higher vantage point to get a better vista of the entire city. However, the climb is punishing, because the terrain is steep so one may want to slow it down. Don't act gong-ho stating that nothing happens to you because it does and its only sensible that you take precautions to ensure nothing untoward happens.
PERMIT OFFICE - yes its an amazing place because well, it gets you to places where there is more amazing stuff awaiting you. the link is http://www.lahdclehpermit.in/contactfl.php. If you choose to make the payment online then, please carry a print out of the receipt page as well as the issued permit. These need to be produced physically at the permit office where they'll issue the hard copy of the permit. Get 3-4 Xerox copies of the permits done immediately as they need to be submitted at the various checkpoints. Now, the most important thing, the permit office is located at the main market area opposite to a J&K bank branch. Easy to locate. Carry an original ID as they may ask to see it when applying there. There is an online form that needs to be filled and the printout is supposed to be carried to the office. If you don't, there is an internet cafe very conveniently located where they can do it for you. For different places you need a different permit. So for Pangong and Nubra or any other place on your radar you need separate permits. If you feel at a loss as to how to go about it just ask the people at the counter. They are very sweet and will tell you the entire process.
TIP - to save on food, have lunch in the bazaar below the Leh Palace. That place is full of local Kashmiri eateries which sell delicacies and I was able to get a full rounded meal in 100 INR. Nothing lavish, but very filling, especially Czot(yes it was spelt like this) with some butter. Get some packed and enjoy it under the sun. I looked for Khatai, which is sweet but found it only in one shop. Its amazing, and pretty soft. Go easy though, can also lead you to an upset stomach if you have one too many.
TIP - the best way to tour Nubra and Pangong is by shared taxi, mini bus. To find the best deal, look for ads in the main market area and there are plenty of ads where people are looking for additional people to tag along with them. Contact numbers are written for you to get back to them. Call up a few and get an idea of the rates they charge versus the vehicle they have, and choose a rate that works for you. All packages are just including your transit cost. For stay over in Hundar(Nubra), the driver shall arrange a homestay for which additional expenses have to be incurred by the stay party. I got a 1 night 2 days package covering Pangong and Nubra for 3500/- in a Bolero, with 5 other people, after some surprising negotiation which I tried simply on the off chance that I may get some discount.