Sadly for you Jane, the best of the (few) Harrogate folk nights is only held once a month, on the first Monday at the Traveller's Rest, Crimple (see other thread).

If I take "mid-week" to mean just Wed and Thurs, then there are some others in the area (as opposed to the direct locality) that might be worth your travelling to - depending on your predilections being for singaround or guest night or tune session of course.
You might like to consider these:
Morley folk club (not-quite-alternate Wednesdays)
The Topic folk club, Bradford (Thursdays)
The Black Swan fc, York (Thursdays)
Otley fc (Wednesdays)
The Park, Wibsey, Bradford (Wednesdays)

Otherwise, the Tykes' News (Filofolk) web-page is also a useful source for upcoming and regular folk/acoustic events, though it tends to cover the folkier side and many acoustic events aren't as widely advertised.

Or - if you were to PM me, Jane, and tell me which exact week you'll be in Harrogate, and what kind of folk/acoustic event you favour, then I could easily look out something specific for you.

Cheers!