I visited Ladakh on 4th october.If you are going by air, then it would take 1 hour 30mins to reach. When you reach you to Leh. You will get many hotels there. i suggest you to prebook your hotel.In leh district, there is one famous market 'Tibetan market'.
secondly, from leh to khardungla distance of 40km.it is not an easy task to cover 40km as khardungla is one of the highest motorable road.You can travel magnatic hill, sangam valley, Nubra valley where you can witness double hump camle ride . and Visit pangong Tso in late.
Firstly, I wouldn't suggest to backpack leh in first solo that too in the month of October. It will be winter start so prefer going there by air than road, as roads to leh gets closed in winters from srinagar and Manali as well. There will be plenty of homestays and hostels in leh. Places to see around are magnetic hill, sangam rafting(if applicable), Leh Palace, Shanti Stupa, thiksey monestry, spituk monestry, shey palace etc. Nubra Valley via khardung La, pangong lake via chang la pass. Not sure about the road conditions though.
Thats a good plan actually in October, i will be there in October also. some tips for your first leh tour
1. best winter jackets
2. good warm gloves
3. good high ankles boot this is the most important packing material you should carry yourself.. and make your itenary simple. 2-3 days keep in your hand for any emergency or acclimatize yourself. some places are very beautiful don't over excitement., stay in your plan. don't forget leh will be leh so safe travel and clean travel. apply your permits on internet and is there any inner line permit you have to visit permit center in leh. must take a BSNL sim card. if you plan in a bike solo, then join any travel groups over there..or you can avoid as it is your first .. enjoy