I went on a short trip to Nepal on Shivratri's long weekend in March 2019. Setting out from Delhi, you can also visit this small peaceful country without taking leaves or expensive flights. This is how you can do it.
Take a train or bus to Gorakhpur overnight on Friday. (See: List of trains that run between Delhi and Gorakhpur)
I would recommend Humsafar Express as it is the fastest and most comfortable train on this route.
Once you reach Gorakhpur, you can easily find a bus to Sonauli border. The Uttar Pradesh State Transport bus stand is just 300 metres from Gorakhpur railway station.
It takes about two and a half hours to reach Sonauli. You can cross the international border to enter Nepal without any documentation or security check.
As you enter Nepal, you find many private tour operators with buses that run to Pokhara and Kathmandu. The journey to Kathmandu and Pokhara takes nine hours and five hours respectively. Alternately, to avoid travel fatigue, it is advisable that you visit Lumbini instead, which is just 25 km from the border.
Itinerary A - Lumbini > Pokhara > Sonauli
The birthplace of Gautam Buddha, Lumbini, is a small town untouched by urbanisation. Maya Devi Temple, the site of birth of Gautam Buddha, is an important place to visit. There are stupas and brick structures and an Ashokan Pillar which date back to 3rd century BC. The complex has been expanded to eastern and western zones with Buddhist structures for communities belonging to Cambodia, Sri Lanka, Myanmar, Thailand, Australia and more. World Peace Pagoda and Lumbini Museum are the other attractions here.
On the opposite end, you can find the Lumbini Crane Sanctuary amidst a beautiful forest of sheesham trees, situated in the middle of a traditional village with wheat fields and mango orchards.
You may choose to spend the night in Lumbini itself or take an overnight bus to Kathmandu. If you spend the night in Lumbini, you can take the early morning bus to Pokhara which takes about five hours to cover a distance of 180 km.