Tramshed, Clare Road, Cardiff, CF11 6QP
Cardiff Central is the closest station, and it is only a 10 minute walk to the venue from there. It will probably take just as long by taxi given the state of the roads, but there are plenty of taxis waiting outside the station if needed!
There are a lot of taxis in the city, and Dragon Taxis seems to have a monopoly on them. We would still recommend pre-booking a taxi for leaving later on in the night, if you need one. The city gets pretty busy on a Saturday night!
Your other option are the apps like Uber, Ola, and Lyft. There are normally plenty on there.
Taxi Companies:
There is pay and display on-street parking outside the venue, and numerous streets nearby.
Other than that, the nearest place to park would be Cardiff Central station, and then a 10 minute walk to the venue.