For a solo traveller, if you start your day from East Sikkim there will be nearly 10 spots to cover which will cost around Rs 3000/- with a hired vehicle. The next day, you can travel to Nathula pass and Tsomgo lake by a vehicle which will cost nearly Rs 5000/- . North Sikkim can be travelled right after East Sikkim. North Sikkim attracts its travellers with Gurudongmar lake, Lachen Valley etc costing Rs 10,000/- along with a journey of 3days and 2nights. Subsequently, you can plan for South Sikkim the other day. The main attraction includes Samdruptse, Buddha park etc. The same will cost around Rs 3000/- The places in West Sikkim are Pemayangtse Monastery, Khecheopalri lake, Goecha La, Varsey Rhododendron Sanctuary etc costing approximately Rs 3000/-. Thus your travel to Sikkim will be Rs 24,000/-.
10k is max. also depends on the number of people traveling. like 8 of us travelled from Kolkata. we left from sealdah in Darjeeling mail reached njp railway station the next day. from their to Gangtok. next day Gangtok sightings, next day nathula, baba harbhajan and tsango lake. after that we left for lachung, covered yumthang valley and zero point. next we left for lachen and covered gurodungmar lake, next we left for peiling which included 3 days more and then back to Gangtok and then njp. so the whole trip of 10 days costed 7500/- per person including travel, stay and food.