Esyllt is my favourite Welsh girls name, but I would avoid this in England due to the Ll.
I'm half Welsh, half English. My Welsh name has been mentioned on here and is usually pronounced wrong (I live in England). It doesn't bother me much, but it does bother my mother, who is a native Welsh speaker (Anglesey) as most of my friends and teachers got it wrong.
For what it's worth I love my name, and I'm glad I have a name which reflects my Welsh heritage. I often get compliments on it, and it's a good ice breaker as people usually say 'oh that's pretty and/or unusual' at which point I can say 'thanks, it's Welsh for X' and that starts a conversation about Welsh origins and family.
As Mike and others have said, you do need to bear in mind whether names will sound rude etc. in other languages. My mother didn't with me and also had Myfanwy (muh-VAN-wee) on her list, which looks quite different to the English eye. Her boys name for me would have been Ynyr, which I struggle to pronounce. My English family can pronounce my name, but I don't think they would have managed Ynyr as well.
Names on my (currently hypothetical) list are:
Alys (Alice)
Eira (EY-ra - ey as in hey and ra as in rabbit)
Aneira (so she could be Anni for short)
Nia (worked with one and it was generally pronounced correctly)
Morwenna (Saint Morwenna was born in Wales, but did her saintly stuff in Cornwall)
Eirys (EY-riss)
Eirlys (EYR-liss)
Enfys (EN-viss)
Eleri (rhymes with Terry)
Tesni (TESS-nee - means warmth from the sun, and she could be Tess or Tessa for short)
Mari (marry, Welsh for Mary)
Aled (easy to say, well known)
Alun (Al-in)
Aneirin/Aneurin (a-NEIGH-rin)
Osian (OSH-an (an as in Anne, not 'un'))
Tomos (TO-moss, both Os pronounced like the O in 'moss'. I would shorten to Twm at home, but he could be Tom if he wanted at school)
Taliesin (Tally-ESS-in)
I think my favourites are Alys, Eira, Morwenna and Tesni for girls and Osian and Tomos for boys.
Pob lwc!