It is quickest, and generally cheapest, to take the train from Leeds to Cambridge. Catch the National Express coach to Cambridge from Dyer Street. There are nine services per day; most require a change in Milton Keynes or Sheffield. There is one direct bus per day, but this is slower than the other service. Either way, the journey will take from 5 ½ to 6 hour 45 minutes. The first bus leaves at 0640 and the last one departs at 1700. A single ticket is 38.50 GBP and a return is 38.50- 45.00 GBP.
After booking online, you will be issued with an e-ticket, which you need to print out and take with you, or an m-ticket, which is sent to your mobile phone. Otherwise you can get at ticket at the bus station. Buses from Leeds to Cambridge can be very crowded at times and there is no guarantee of a place unless you book in advance.
There are between 1-3 trains per hour, and you need to change once (in Peterborough) or twice (Peterborough and Ely). The journey takes between 2 hours 30 minutes and 2 hours 50 minutes. A single ticket is 21.50 GBP or you can get an off peak return for 66.50 GBP.
The UK train ticketing system is notoriously complicated. It is usually cheaper to buy your tickets up to 6pm on the day before you travel than on the day. And fares are more expensive if you travel before 09:30.
On arrival in Cambridge, it is a 15-minute walk to the town centre, or you can catch a taxi outside the station for around 5 GBP. There is also a bus that runs about every 10 minutes.
To walk, exit the station and continue along Station Road, which is directly in front of you. At the T-junction, turn right onto Hills Road, which takes you towards the city centre.
If you are looking for a deal on accomodation on arrival in Cambridge why not check out some hotels deals: