How quick a look on Google? It should have given the rather smart Bournemouth tourism website at http://www.bournemouth.co.uk

Use the Accomodation search, click Area, select Central East and when the result list appears click the option "Show as Map" (left side, top of list). You can fine tune it by selecting Type as well but there's always a grey area between small Hotels and bigger Guesthouses so it may be worth going through the whole list.

Sue Bournemouth is literally full of hotels. If you look at the map and find the BIC near the pier, the area behind and to the west is where many of the hotels are.
This is a short 10 min taxi ride away from the train station.
Cheaper accomadation will come up in Boscombe but its not a very nice area.
Hope this helps , please let me know if you have any more questions. Cant help with hotels as we live fairly localy.
J

Thank you both for your helpful replies.
I really just wanted to know which is the best area to start looking for hotels/BBs.
I had gone on the Google map and gone up and down several streets and had even found one of the Wetherspoon pubs which we always like to visit, without even searching.
The Bournemouth website is indeed excellent Steve.

Many thanks
Sue