I recommend you to stay there many days, then you can visit different cities in the same trip, that's what i do in my UK trips.
I should recommend you Leeds or London.
Leeds: There are some cheap hotels. You can also visit other cities like Sheffield, Hull, Bradford, Shipley Glen...etc... There are many trials riders and very nice people, you will feel more than welcome like i felt.
This is the hotel that i always stay, cheap, clean, very comfortable, big rooms...: http://www.ibis.com/es/booking/hotels-list.shtml
London: Very expensive hotels. You can also visit other cities like Bristol, Portsmouth, Plymouth, etc... But the train transport in the UK is the most expensive i've seen ever.
It's one of the most beautiful cities i've seen.