Trips from Bhubaneswar
Bhubaneswar has Puri and Konark within about 1.5 hours, and Chilika Lake a little further. For the mountains, Darjeeling and Sikkim are reached by flight to Bagdogra, usually via Kolkata.
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Tour packages from Bhubaneswar: route guides
How to get there from Bhubaneswar, how many days you need and a day by day plan for each.
Best weekend trips from Bhubaneswar

Darjeeling
Tea gardens, toy trains and sunrise over Kangchenjunga
Fly to Bagdogra, usually via Kolkata, then about 3 hours by road.
Longer trips from Bhubaneswar

Andaman Islands
The clearest water in India, and the best beach most people never reach
Fly to Port Blair, direct on some days or via Kolkata or Chennai.

Goa
Beaches by day, everything else by night
Fly, direct on some days or with one connection.

Gangtok & Sikkim
Kangchenjunga, high lakes and the cleanest hill state in India
Fly to Bagdogra, then 4 to 5 hours by road.
