There are three options, Bus, Taxi, and Train.
The bus is cheap, but not nearby and not big luggage-friendly. There are 2 direct buses to Vrindavan per day. They leave the Sarai Kalai Khan Interstate Bus Terminal (ISBT) at 9:30 AM and 3:00 PM and arrive in Vrindavan about three hours later depending on traffic. There are several ISBT stations, so be sure to tell the rickshaw wallah that you want the Sarai Kalai Khan (ISBT). The cost is about Rs 90, depending on the bus company that owns the bus. They leave from bay 56 which is in section F of the bus terminal. There are some seats in the shade and a water and juice booth nearby if you end up arriving early for the bus. If you are arriving at another time after 4:30 AM and before Midnight, you can take any Mathura or Agra-bound bus and request to get down at Chatikara road, which is the main road into Vrindavan.
As you enter the ISBT, there is an overpass (fly-over) where the outbound buses generally loiter trying to pick up more passengers. If you would like to save some time, ask the rickshaw wallah to ask the conductors of those buses if they are Agra or Mathura buses, and if they are then get on that bus and don't bother going to the terminal itself. If you are taking a Mathura or Agra-bound bus, you will need to take a rickshaw, auto rickshaw, jeep, or tempo into Vrindavan from the intersection of the highway and Chatikara road. If you stand at the end of Chatikara road there will generally be one of those along shortly, but again luggage may be a problem as except for the autorickshaw the others are not usually equipped to accommodate large pieces of luggage. As before, if there is space available, you could buy it a seat. The Agra busses make a rest stop at a roadside eatery (dhaba) just before the U.P. border which lasts 10-15 minutes. If you arrive at Chatikara Road after 8:00 PM it is wiser to go on to Mathura and get to Vrindavan from there as the rickshaw, auto rickshaw, jeeps, and tempos are infrequent or not running after that time. There are four direct buses to New Dehli Sarai Kalai Khan (ISBT), at 5 AM, 9 AM, 12:00 Noon, and 2:00 PM. The buses leave from the Vrindavan bus stand, which is a Rs15 rickshaw ride from anywhere in Vrindavan. These buses may break down from time to time, so leave plenty of time for your connection if you decide to try this option. Depending on the bus, there is not a lot of provision for large articles of luggage. Any amount of hand-luggage or carry-ons are fine as there is space under the seat and overhead bins which are seldom used and provide a lot of space. There is generally some room around the engine hump in the front of the bus for a decent-sized suitcase. In the worst-case I suppose you could put your luggage on a seat and pay for it as a passenger. There is room on the top of the bus, but the driver is extremely unlikely to suggest or assist in any way putting your stuff up there.
The buses from Mathura depart from the Mathura Bus stand and are a little more expensive than the Vrindavan buses because the distance is a bit more.
A taxi can be arranged with the hotel or by phoning up the taxi companies in Vrindavan. This would need to be done a day in advance for a Vrindavan taxi. In my experience the hotel taxi quotes are over-priced. They will tell you all about the taxes they must pay for crossing into Harayana and Uttar Pradesh, but this is hardly your concern. Travel to Mathura or Vrindavan by taxi late at night is not a good idea because most of Vrindavan shuts down early. The Mathura and Vrindavan Maths are locked up tight from about 10PM until about 5AM. Best is to stay overnight in our Math in Delhi, have a good rest and leave next early morning at about 6 am, before you get stuck in the helly, smelly Delhi traffic.
If you are looking to economise then I would suggest the train, especially if you are traveling alone during day time. There is an efficient Tourist booking office upstairs in the New Delhi Railway Station. They are open daily 8:00 AM to 5:00 PM Monday to Saturday and 8:00 AM to 2:00 PM Sunday. They close for a break from 2:00 PM to 2:15 PM. The queue (line) for paying in dollars or pounds is on the left, rupees on the right.
The dollar/pound queue may be shorter. You will receive you change in rupees. If you have some small paper dollar or pound currency it will save you some time waiting for change. Railway Ticket Classes Types of Class Codes AC 2-tier sleeper Code: 2A First class Code: FC AC 3 Tier Code: 3A AC chair Car Code: CC Sleeper Class Code: SL Second Sitting Code: 2S.
There still there may be some unscrupulous travel agents across the road from the railway station who may approach you in front of the station or inside to persuade you to come to their shop by telling you that the Tourist Booking Office is closed or caught fire. They are big cheaters. Ignore them. You can book a tourist quota seat or seats on a train going to Mathura up until four hours before departure. After that time, the seats are released, and there is a place out in the front of the station called "Current Reservations" (it looks like an ice-cream stand) where you can book a sleeper-class ticket within two hours of the time of departure. It is advantageous to buy the ticket at current reservations as it entitles you to wait in the second class sleeper waiting room, which is much more pleasant than waiting on the platform. There are almost always sleeper seats available to Mathura, because passengers will be boarding the train at Agra (home of the Taj Mahal), which is the next major station after Mathura Junction. If you are paying in rupees, you can also go to the computerised booking office on Chelmsford road. It is a very large hall with many booking windows. As you approach the booking office a booth outside on your right where you must obtain a booking form.
Fill in the form and present it and pay at any of the booking windows. This office was almost deserted when I was last there, but can be very busy. It is airconditioned. Bookings made any regular computerised booking office do not have access to the tourist quota, which may be a problem if you are trying to book a ticket on a popular train at a peak-period. I've never used this service, but it is also possible to book your ticket on the internet, pay by credit card, and collect it at the Chelmsford road computerised booking office. The window for collecting the tickets is on the far right inside the booking office. This service is only available at this location. Inside India the tickets can be booked on the internet and sent by post, a maximum of six tickets on any train, and a maximum of four booking per month. If you have a second sitting ticket and want to upgrade, it is wise to speak to the TTE (Traveling Ticket Examiner) on the platform before boarding the train. They wear a dark suit with a distinctive Indian Railways red necktie with a Gold "IR" in a circle emblazoned on it. They can be seen scurrying around with a computer printout in their hand. They will indicate which coach you should board and may assign you a seat on the spot. They will come around and collect the difference in fare some time after the train departs. If you already have a sleeper class ticket they will come and look at it some time during the journey. Inside the station, you can only buy a second class unreserved ticket Rs 43 to Rs 57 (and upgrade to a sleeper ticket on the train for an additional of about Rs 100) but you may have to wait in a big line (queue) of impatient and pushy Indians to do it. This will certainly prove interesting, but you'd be better off getting a SLEEPER ticket (Rs. 180) either upstairs at the Tourist Booking Office or out front at "Current Reservations".
Second class unreserved is a wooden park bench in a cattle car. Usually there is nowhere to sit and nowhere to put your bags, so it's much more comfortable with the sleeper car, a guaranteed seat and there will be a place to put your bags either under your seat or up above opposite you (where you can see them) in the upper berth. NOTE: It is worth the extra money (if you have) to book an Air Conditioned 3 Tier Sleeper coach seat (about Rs 450), especially for the return journey from Mathura to New Delhi. The reason for this is that Mathura is toward the end of the journey of many New Delhi bound trains, and the TTEs become a little more lax about enforcing the rules about Second class unreserved passengers occupying seats (and every other available inch of space) in the non-AC second class sleeper cars. So, you may have a reserved seat, but no way to get to it. This is the voice of experience speaking. Going from New Delhi to Mathura I have never encountered this problem. Alternatively you can book the Taj Express which leaves at 7.10 am from Nizambudim train station, which is all Second class unreserved, usually crowded, fast, and at Rs 90 or so, quite a bit cheaper than AC3. There are still the luggage logistics problems of Second class unreserved coaches, though.