I genuinely appreciate your reluctance with regard to paper publications, Anne, but in the case of the NE region Folk Roundabout magazine really is the only genuinely reliable source for the kind of listings you need.
The majority of clubs are of the "chances to perform" type rather than "floor spot" as such, but I could personally recommend The Brit at Darlington (on the Tues) and either The Welly (Wolviston) or Durham Folk Club (both on the Thurs).
It really is worth getting a copy of the magazine for future - and continued - reference though, for at £1.50 it is excellent value in this day and age and pretty darned accurate. And yes, the above post is correct in that so many web entries are woefully out of date. Beware...