The best database of accommodation in the area is probably this one:
http://www.visitnorthumbria.com/index.cfm?fuseaction=sea rch.accommodation&categoryid=82
Under 'Where would you like to stay?' set the left hand box to 'Tyne & Wear' and the right-hand one to 'South Shields'. You might choose to accept the default setting of 'within 5 miles' but I suggest trying something a bit bigger.
A word of warning, though. When using that search facility, have a map to hand because the search engine ignores the presence of the River Tyne when calculating distances!
If you can't find anywhere in South Shields itself, you might want to consider places on the south bank of the Tyne, such as Jarrow (9 minutes), Heworth (19 minutes), Gateshead or even central Newcastle (28 minutes). Those times are for journeys on the Tyne & Wear Metro which operates fast and cheap trains,four or five times an hour, seven days a week.
Another alternative would be to consider North Shields. It might be, however, that the Shields Ferry doesn't run at suitable times for you. See here for the timetable:
http://www.tyneandwearmetro.co.uk/PDF/Ferrylink%20Leafle t%202.pdf
(It takes an age to download!).
Finally, in case you've not already tried these places,I'll give you this link to five guest houses in South Shields:
http://www.southshields-sanddancers.co.uk/accommodation. htm
Hoping that something here is of use to you,
Chris