-what are some things we should be aware of when booking? It depends on where you want to go and what you want to do.
-when is the best time of year to go?
Any time is good. You will find that the really popular tourist locations like York are much fuller on bank holiday weekends, and weekends in the summer. If you're going to the National Railway Museum then be aware that in the school holidays it will be full of small boys. Also please bear in mind that the weather is likely to be a lot damper than you are used to. In winter this is especially noticable.
-should we try black pudding?
Yes unless you are really squeamish about blood. I love it, myself.
-would it be better/easier/cheaper to fly into london and take the train from there or fly into leeds?
If you get a train, make sure you book well in advance as rail fares can be extortionate. Internal flights can also be an option, and can be cheaper than the train. There are bus services, but they take longer than the train or flying.
-should we give up trying to do it ourselves and book with a travel agent?
It depends- more on the US than on the UK (eg what protection you have if there is a problem with the airline or whatever). It is entirely possible to do it yourself, and the Tourist Information Service for the places you are visiting can be really helpful, including lists of accomodation providers. B&Bs provide good, cheap rooms- usually with a full english breakfast provided in the morning.
-any tips on accomodations?
Bed and Breakfast places can provide great accomodation at low prices. Do book early as they can get full quite quickly during busy periods- as can hotels. You also often get to meet your hosts, who can provide further information for you. Pubs sometimes have bed and breakfast accomodation too. Youth Hostels are also good- although you will often have to stay in separate male/female dorms, and do a small chore. The good thing there is that you get to meet people. Another relatively cheap option is a cheap room in a chain hotel like Quality Inn or similar, although they don't provide breakfast, and tend to be outside the town/city centres.
Whatever you do, do try to book in advance. Most places will let you do it online, and may have special offers for early booking, or midweek/weekend packages.