Lots of do in every direction except south.
From Swansea you can ride the Rhigos loop by heading towards Port Talbot, up the Afan valley road, over the big summit, down the other side into teh Rhondda then over the Rhigos and back down the Neath valley (back road). Great 3.5-5hr route over some big hills.
Or head up over the Black Mtn and choose a loop back (lots of options).
Or go to Carren Cennan Castle for a fantastic tea shop and great riding.
Cycle to Aberystwyth over the devils staircase and telephone box hill (about 95miles), stay over, then return the next day by a flatter route through carmarthenshire.
The moors directly north of swansea all also good, albeit very steep. Access from near Morrison hospital.
Swansea Wheelers Cycle Club do club runs on all of the above and used to have lots of routes available to download on their website.
For a flatter ride head to Porthcawl .