As said Llantrisant is upstairs, but they are not steep. The club is on an excellent website - www.folkwales.org.uk
The Lyceum in Newport has steep stairs. and the Norwegian Church has a level access.
On the the second Tuesday of the month is the BBC club (Llandaff) with level access.
There is a blues club every Thursday in the Gower in Cathays, again upstairs, but I've not been there so I can't report on steepness
There is an Alt-Cardiff night usually on the 1st Sunday of the month at Chapter Arts Centre in Canton, upstairs but with a lift, the style of music is towards the newer country/songwriter type, recent guests have been Chip Taylor & Carrie Rodriguez, The Mekons, and Fred Eaglesmith.
Fridays there is a smokey folk cum country night at the Blue Dragon Hotel, Newport Rd, Roath. A few steps outside and inside.
There is also an excellent Rockabilly session at the Pilot in Penarth, level access as far as I can remember.
Taplas magazine, as mentioned by Sian, is excellent. There is also a freeby monthly listings magazine called the Buzz. The Echo has its moments as well.

And don't forget Miskin at Easter.

All the best, and hope to see you at one or other in the near future.

Oh, and I almost forgot a bit of shemeless self-promotion - Resonator (classic Americana) at Cafe Europa, Castle Street, 1st Thursday every month!

All the best