Blackfriars is north of the Thames, but barely. In fact, it’s an interesting station as the platforms are on a bridge over the river and you can leave the station from either end, that is on the south bank or the north. The picture below is from the north looking south.
Some trains terminate (ie finish) here, some pass through.
The station has been re-built and modernised quite recently. Trains come in from Kent, and Thameslink serves this station, so Luton and Gatwick airports, Croydon, Brighton, St Alban’s and so on. It’s a busy station during the week, with city workers forming a healthy rush hour.
Underground
Out of the north end platforms and then down to the Circle and District lines, again to Victoria, Bayswater, King’s Cross and so on.
Bus
There’s no bus station, but the 40 and 63 go past outside.
The 40 goes to Elephant and Castle and Dulwich in the south and Farringdon (for Elizabeth Line etc) in the north.
The 63 goes to King’s Cross in the north and Peckham in the south.
Taxi
This may be the best choice for central London. It’s not so far, and the ride is scenic.
It’s pushing it a bit to say there is a taxi rank at the front of the station, but there is a dedicated and marked space for taxi cabs, so look there. The roads nearby are busy so taxis should be plentiful.
If you have time…
It’s an historic area. The Thames is inches away.
On the south bank there’s Tate Modern, the Globe theatre, lots of nice hotels and a short walk to the South Bank arts centre.
On the north bank is historic London. St Paul’s Cathedral, The Old Bailey (criminal courts), lots of old and lovely pubs, Fleet Street… so much to enjoy and maybe worth a visit anyway.