Nope..1 full day isn't enough for Darjeeling. At least 2 full days needed for explore Darjeeling.
Day 1 : Tiger Hill, rock garden, Mall and other local side seen where you want to go. Day 2 : Experience World Heritage Toy Train, Ghum Monastery, Batasia Loop. If you want to teste some delicious foods, then you have to visit Sonam's Kitchen (for Breakfast), Keventers (for Breakfast), Glenary's Restaurant (Lunch/Dinner), Kunga( for Dinner) And you have a plan to go Gangtok. then you must go to Lamahatta natural lake and Tin-Chulay tea states. two small village near Darjeeling (on the way to Gangtok)
One day is not enough for darjeeling, you will miss many things, i think you must drop the plan to visit sikkim, sikkim is not 2hr but 4 hr from darjiling, you won't be able to enjoy sikkim/ gangtok, so its better you stay at darjiling and enjoy it to the fullest.
If you have just one day in Darjeeling then better start your day early morning to catch up sunrise in tiger hills, it's beautiful. Then you can start exploring from ghoom, there is a Tibetan monsatry, then to gangchen, zoo and some museums around. Don't forget to have blissful breakfast at glanary.
One day is never enough to visit any place as per my opinion. Being known as one of the tourist destinations, Darjeeling has many sight seeing locations and activities, for example, rope-way, Tibetan Refugee Camp, Himalayan Tibet Museum, Zoological Park, Tea Estates, etc.
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