There is some airlines flying to a place called Simara from where it takes around 45 minutes to reach Birgunj. If you have hotels booked then there is possibility of pick up from the airport to the hotel or you can hire some cabs. If you want to travel by land then there are several buses leaving from Kathmandu and some are really good services. There are also night buses leaving from kathmandu to birgunj and these are the best buses running in Nepal.
Travel by Tata Sumo (jeep) from Birgunj to Kathmandu takes 5-6 hours and is a bumpy ride at best--perhaps not for the faint of heart. The ride should cost INR250-350 (NPR 500).
For more details on crossing the border from India to Birgunj, see the information under 'Get Out' on it's Indian sister's town page Raxaul.
Though it is not a tourist hot spot, you can see Lord Buddha stupa on a tiny hillock called Vishwa. Apart from this, Gadhi Mai is a well known Hindu Goddess temple which holds a mighty fair every five years. Hindus from all over the world come here to sacrifice animals to show thankfulness to the goddess.Animal sacrificed on this occassion is one of the highest amount in the world. To the west of Birgunj, Bindawasni mai is another historical and religious place. Jang Bhandur Rana, the first Rana prime minister held a massacre in which hundreds of people died as a result of royal conspiracy. To the north of the city there is Parsa Wildlife Reserve, one of the biggest national park having 100s of endangered species. Tigers,elephants,musk deer, Gharials, Red hornedbills Etc are main attraction.
If you're looking for a local Ncell SIM card, Birgunj has an official Ncell store halfway up the main road on the right from the border as you walk towards the large tower in the middle of the road. They speak perfect English! For more information about telecommunications in Nepal, have a look under the 'Contact' section in Nepal.
There are very few 'restaurants' in Birgunj. Most food is street food, but there are restaurants serving a variety of western, Indian and Nepali food attached to most hotels in the city.
An abundance of mosquitoes in April, together with heat of 40C, made sleep almost impossible in early April.