As long as i already mentioned Nepal, I'd be happy to share some Indian-visa-in-Nepal experience.
And I have to say, that this is the thing i can hardly recommend you to do.
It's tuff, absolutely not convenient and you never know what the result is going to be. So if you need more than 1-2 months Indian tourist visa, you better go somewhere else.
In some of my next articles I will share the same experience with Laos which was way much better.
First of all, when coming to Nepal you don't need to bother with Nepalese visa itself. They can put one into your passport right at the airport within about 15 minutes. The fee will depend on how long are you going to stay, and if it's just for two weeks, it would cost you less than 30 USD.
The airport itself is one of the most unconvenient ones I've ever been to. But at least you can buy a sim-card right at the airport as soon as you arrive. It usually starts working at the same moment, so you don't have to worry about access to the Internet. It's nice if you don't know where are you going to stay.
But remember, for getting it you must provide your passport and visa copy and one small photo. They can actually make a copy of the passport themselves, but if you don't have a photo you're not getting the sim-card.
If you don't have any hotel booked you better go directly to the Thamil area, it's a kinda nice touristic downtown area where you can get everything you need, including the room, food and souvenirs. I extremely recommend to get some organic Nepalese coffee and tea. It's really great.
But let's go back to getting Indian visa.
There are many agencies just next to the visa centre which can help you with all documents for some fee. But i personaly recommend to prepare everything before you come. Here is the website where you can get all the information you need about the embassy and the application form which you are to fill.
https://www.indianembassy.org.np/index1.php?option=Xgc4cACnML2T1_DC21jA58Ttm2KiX8IXemmj5VvU8ug&id=e5igN5n3-J8xIGeBkAfQuDckTeqRyV07jACWKpK__jE
First of all you gotta go fill up the application form online and get it printed more likely if you have a printed photo 3x4 or little bigger size similar to the photo downloaded into your application form. You also have to provide your tickets to India and back, passport copy, Nepalese visa copy and a kind of a document from your bank account proving that you have enough money to stay in India during the time you're applying for. You can easily make your "tickets" and "bank details" in photoshop as i did. It's just a formal stuff which no one will ever check.
So the first time you come early in the morning and give all your documents to apply for a new visa. They won't take your passport and money this time, but will tell you when to come and find out whether they approve your application or not.
Then you come there again, and if everything is okay, they will take the fee (as far as I remember it was 56 USD) and passport and let you know when to pick it up.
The funny thing is that they won't tell you how long your new visa is going to be valid. They can give you as much time as they decide and never care about duration time you are applying for. You probably won't know until you get your passport back.
Both times you'd better come as early as possible, because the line is freaking huge and super slowly moving. The good thing is that it's only 20 minutes walk from Thamil, so if the weather is nice, you can get a beautiful morning walking through the Khathmandu downtown.
The third time you come in the evening and usually there aren't so many people. You're just getting you passport and it takes not so much time.
What can I say.. When I was there the embassy worker was rude and unwelcoming, the duration of getting visa was longer then it was claimed, so i lost quite a lot money because I had to change the tickets, so the impression is quite ugly.
But Nepal in general and Khathmandu itself is worthy to see, no doubt.