I knew it would be there somewhere !! Athlone is fine - quite common not to give a street name if they lived in the town.
You mentioned earlier that the marriage took place in St. Mary's, which is the Westmeath part of Athlone. The western part of the town was on the other side of the river Shannon and in Co. Roscommon.
I suspect that Jane's birth was just before 1864 or simply never registered, but what you could try is a birth for one of her siblings to confirm some details on the family. I think I'd try Margaret - the possible witness - hopefully it will show her father as a Labourer with an address in Athlone town.
These are the references you need to order a research cert for her :
Name: Margaret Crawford
Event Type: Birth
Year : 1868
Registration District : Athlone
Volume: 8 / Page: 2
I dont think there wouldn't be that many Thomas Crawfords with occupations labourers in Athlone town at the same time, so you might be able reasonably link to your Jane based on that.
for notes on ordering a research birth cert see :
Ordering Certs from GRO Roscommon Details included on a Birth CertThat Griffith's reference you mentioned is in a separate district named Ballymahon, which is about 20km to the north est of Athlone, so not sure that would be connected. Your Thomas may not have held is own property at the time of Griffith's