MIMS, Herts > America, 17th century
I am afraid I cannot help very much with this one, except to refer you to My Ancestors Emigrated from Hertfordshire.
An English surname such as Mim(m)s may have originated from someone who had come from a place called Mimms in perhaps the 14th century and by the 17th century there is unlikely to be any significant geographical connection between the surname and the place the family left behind three centuries or more before. Of course people change their names but it is often to conceal their origins rather than to advertise where they came from. You may find What did your Ancestor call himself of interest.
Another complication is you say that Tomas Mims came from Wales and was born in Hertfordshire without giving the source of your information. While this is possible, Hertfordshire is a long way from Wales while Herefordshire has a common border with Wales - and it is not uncommon for amateur genealogists to confuse the two. .
If you can add to the information given above tell me.