Hi,
I can see the family on censuses from 1861 to 1891 -
1861 - In Brynsciencyn, Anglesey Evan 26; Mary (wife ) 29 with sons Thomas 4 and Evan 1.Mary seem to originate from Llangeinwen and Evan from Maltreath - both in Anglesey.
1871 - In Well Street, Llanllechid, Evan 36 Mary 37, Thomas 13, Evan 11, Mary 8, Owen 6, Emmanuel 4 Robert John 10 months.
1881 - In Goronowy Street, Llanllechid - Evan Evans 47, Mary 48, Thomas 28, Mary 18, Owen 16, Emmanuel 14, Robert 10, Evan 7.
1891 - Still in Goronowy Street, Evan 56, Mary 58, Emmanuel 24, Robert 20, Evan 17.
If you look for a death of the young Evan (born 1860) it looks like he died in 1873 age 13 - Free BMD has a death for Bangor District Mar Qtr Reference 11b/418 which may be him.
If you subscribe to the Ancestry genealogy site you will see a number of family trees relating to some family members - perhaps you would be able to contact them prior to your visit? I haven't checked them all but for example one tree suggests that Owen Evans died in 1924 in the Bethesda area. It is also suggested that the father of Evan Evans (born c1835) was Thomas Evans (c1802) with his father being an Emmanuel Evans.
It looks to me there is a quite a big family out there waiting for you to find them.
Hope this helps
Alan
Another god source to look at is
www.familysearch.org which may help you to find more information.