I have walked several sections of the Wales Coast Path. Don't assume that this is an entirely scenic path ALL the way around Wales. (One part even goes through the Steelworks town of Port Talbot). However, most of the Wales Coast Path does indeed pass through scenic areas. I would concentrate your attention on the best bits and these in my opinion are found in south-west Wales (Pembrokeshire & Ceredigion).
Assuming you do not have a hire car: take the train from London > Tenby *(suggest you book 2 nights). Only on summer Saturdays does a direct train go from Paddington to Tenby; the rest of the time you will probably change in Swansea. See www.nationalrail.co.uk
Take a boat ride from Tenby to Caldy Island. http://www.caldey-island.co.uk
From Tenby, you could start walking the coastal path going westward. Manorbier & Freshwater East will be the next places with accommodation. Continuing W, you reach Stackpole Quay & then proceed to Barafundle Bay & the Bosherston lily pools. (You might wish to have accommodation in this area). Spectacular cliff formations are found between St.Govans & the Stack Rocks / Green Bridge of Wales. Walking is easy on this section as the land is more or less level. Unfortunately, it is within an army range as is closed to the public much of the time. (Usually open in August & at weekends).
From the Bosherston area, I would take a bus to Pembroke (see Castle) & then another bus to Haverfordwest. Now, you could go out to Dale or Marloes & walk that area & proceed around St.Brides Bay towards St.David's or take a bus from Haverfordwest to Solva (overnight stay), and then walk westward. Here are some coal bus routes:>http://www.pembrokeshire.gov.uk/content.asp?nav=838,1629,839,1038
From St.David's , you could walk all the way up to Fishguard - which has trains that will take you back east.
However, should you wish, you could go by bus from Fishguard to Cardigan and then start walking the Ceredigion section of the Wales Coast Path. Mwnt would be a good starting point or , perhaps base yourselves in Llangranog for a couple of nights and walk both north & south from this village. (The path here has steep inclines).
As an alternative, you might like to try walking in an inland part of Wales. It would, for example, be relatively easy to catch a train at Fishguard and travel all the way across south Wales to Chepstow & then start walking up the Wye Valley. However, I did a section of this path near Tintern & found it rather boring as it was stuck under trees for quite a distance.
The Offas Dyke Path is mainly on upland.
This site will tell you more about Welsh long distance paths. I would also explore the places mentioned using Google Earth.