I would beware of route finders that are most likely to tell you to go from Chepstow to Conwy via the motorways of the Midlands. You may well be on motorways (interstates) but this is a long way round, less scenic and congestion is likely - especially near Birmingham.
If it were me, I would leave Chepstow & take the B4235 towards Usk - where I would join the A449 expressway going N (towards Monmouth) to leave at next junction for Raglan - loop around roundabout on A40 & visit castle. After Raglan Castle - you have to turn left on exiting drive but then loop back to the westbound A40 to Abergavenny > Crickhowell > A479 (see TRETOWER COURT) - head toward Talgarth & then follow A470 all the way up through the middle of Wales to Conway. (This is a scenic route).
Consider staying near Porthmadog if you wish to shorten this long trip. (Don't forget that Wales & Scotland have a separate forums. You might wish to check out the Wales forum). The above assumes that you have already driven up the A466 in the lower Wye Valley to Tintern. Now look at this map:>https://www.google.co.uk/maps/@51.6681178,-2.693743,13z/data=!5m1!1e1
Can you see the village of St.Arvans? If you take the first left after leaving the village - going N on A466 - you will see a minor road marked WYNDCLIFF. If you drive up this for about 3 minutes you will come to a parking area. Park-up and follow track up hill through the woods. After about 15 minutes, it levels off - walk to the right to see a wonderful view over the Wye Valley from Eagles Nest lookout. (If you click & drag the map northward towards Monmouth, you will see ‘Area of outstanding Natural Beauty’ written. Here you will find the YAT ROCK VIEWPOINT). I suggest you drag the yellow man onto the map to see the street view to get an idea of what the roads are like. Do this in the different areas you are likely to visit.
If going by train from Chepstow to Conwy, the best way to go is west to Newport where you can change for direct trains to Conwy. www.nationalrail.co.uk
http://cadw.gov.wales/daysout/raglancastle/?lang=en
If visiting Raglan Castle & intending to take A40 W to Abergavenny, you must leave castle - turn left onto A40 and then left into Groesenon Road before turning R to get onto westbound A40. It is confusing - see >https://www.google.co.uk/maps/@51.7687893,-2.842549,791m/data=!3m1!1e3
(You can learn a lot from maps like this - especially trying to get familiar with the places you might have difficulty).