So, it is Bath to Penmaenmawr! Basically you have a choice of 3 routes. The first thing you need to do is get out of Bath = take A46 N to the M4 (M=Motorway = Interstate in American). Then M4 west towards the Severn bridges. Now, if you want to stay on motorways all the way, you need to take the M5 going NE up to Birmingham and then the M6 going north. You will finally see a route going west to become the A55 expressway along the north Wales coast to Penmaenmawr. (Chester is well worth a stop). Anyway, the trouble with this route is that it can be a bit boring and jams can happen - especially around Birmingham. However, it does have the best quality roads.
The second possible route is to cross the Severn on the M48 bridge and come off at the first junction on the Welsh side and take the A466. This has the advantage of taking you up the scenic lower Wye Valley - see the ruins of Tintern Abbey. (The road is very bendy).
Anyway- continue north passing Monmouth and on to Hereford (which can get congested). The A49 going N - stop at LUDLOW - real ye olde world England. About 1 mile N of Ludlow - visit STOKESAY CASTLE (on left). Then continue N on A49 - skirting Shrewsbury - A5 and then A483 towards Chester to join A55 expressway.
The 3rd possible route (& most scenic) is to cross the Severn on the M4 bridge and leave M4 at J24 (just E of Newport) and take A449 expressway to RAGLAN (which has a ruined CASTLE - but be careful on exit to carefully follow signs to get back on westbound A40 towards Abergavenny) - zoom down on map that follows to see road configuration at Raglan). A40 expressway to Abergavenny - be careful at confusing double roundabout south of town. Then A40 to Crickhowell - turning R onto A479 just N of town. (Visit TRETOWER COURT)? Continue on A479 through the Black Mountains and then follow signs at Talgarth for A470 to Builth Wells. Stay on A470 all the way to Llandudno Junction and proceed west to Penmaenmawr.
It is quite a long haul from Bath to Penmaenmawr. To be honest, it would have been better to have spent the night somewhere mid way and made more of seeing places en-route. Please use the map that follows and zoom down on the routes mentioned at various points to see the roads on street view. This will help you determine which route you think is right for you.
https://www.google.co.uk/maps/@52.3596566,-3.2439946,8.5z/data=!5m1!1e1
You can check out driving times for the routes here:> http://www.theaa.com/route-planner/index.jsp
PS. When staying at Penmaenmawr, from the nearby village of Abergwyngregyn - a minor road leads to a parking area. From here, you can walk up the valley to Aber Falls.
Google places mentioned for more info. Also go to the Wales forum and read some of the other posts there for more info on Wales.
www.visitwales.co.uk