Hi Ruthie,
I am not too familiar with Liverpool itself, but just along the Northern Line is Southport. Home of the Bothy Folk Club which meets every Sunday and has for 40yrs. Tonight we have Cloudstreet. Tomorrow night we have our monthly Monday music session in 'The Guest House' Union St, Southport.
I don't know of any Border sides in the area apart from Stone the Crows from Leyland. The Argarmeles Clogs Ladies N/W side, practice tuesday nights at the Gild Hall, Formby, (see the website for contact details). This is the distaff side of Southport Swords and we can sometimes be seen dancing out together. There are regular monthly ceildhs at Horwich nr Bolton but this may be a bit far away for you.
There is a sing around type of club at the Ship Inn, Haskayne, nr Maghull on Thursday nights, and on Tuesday nights there is a folk club at Maghull, Maghull Folk Club who have their annual Maghull Music Day coming up shortly. Great value for money with Tanglefoot, Mrs Ackroyd Band, Malinky, Flossie, Colum Sands, Bill Whalley & Dave Fletcher, Marie Little, The Spikedrivers, Tony Gibbons & Kate Bradbury. Be warned tickets always sell out in well advance.
I hope this is of help to you, if you want any more info about the dance/music scene N of L/pool PM me.

Cheers
Les
PS I may not get to tonights and tommorrow nights events due to my suffering from an attack of Shingles, (my forehead looks like a Klingons!)