Welcome to Suffollk
You are absolutely right there are a great many Nunn's and a lot of them lived in the parishes around Mellis according to the Suffolk Burial Index.
Yes according to the Suffolk Marriage index he married Mary Downing on the date you state in Mellis. There is nothing to indicate either of them came from outside of the parish.
I have tracked down Robert Nunn wdr on the 1851C living in Mellis - gives his yob as 1974 & his pob as Mellis. He has with him 2 sons William 1828 & Job 1834.
in 1841 Robert c1796 & Mary c1801 were in Mellis with children
Harriot 1823, Thomas 1824, George 1830 & Job 1833.
William 1828 is not with them in 1841 but there are 2 William Nunn's listed on the census in 1841 both in the Hartismere District one obviously part of a family living in Thornham Parva just down the road & the other living in Mellis with a John & Sarah HAMMOND. He could have been lodging with them, he might have been employed by them or they might have been relations but there is no way of telling.
The Suffolk Burial Index lists a Mary NUNN buried in Mellis 5 February 1851 age 49, which would tie in with the yob given in 1841 & Robert stating he is a widower in 1851.
I also found a Robert Nunn c 1795 born Eye on the 1851C living in Bury St Edmunds - described himself as a 'Prof of Music & Dance.
I haven't yet found Robert (Mellis) Nunn on the 1861C but Robert (Eye) Nunn is still living in BSE still with his music.
In 1871 Robert (Mellis) Nunn crops up again aged 81 living at the Falcon Inn, Mellis but he doesn't appear in 1881.
The Suffolk Burial Index gives a Robert NUNN, abode Eye UH, buried 8 Feb 1877 age 89 buried at St Mary, Mellis.
It looks like, if your interest is Robert, Mellis, he was not born in Eye as from the 1871C he was stating his pob as BURGATE, which is a mile or so down the road.
Familysearch pilot notes a Robert NUNN bpt 9 Sept 1798 parish of Burgate son of Daniel & Martha NUNN. Family search lists quite a few children for that couple.
K
ps. Found him in 1861 - living in Dam Lane, Mellis name has been transcribed as something that looks like 'NUME' & my census provider has interpretted it as RUME - thats Suffolk for you - gives his pob as Burgate then as well.