I had to check back to recall, but I first found my Breen ancestor from Clare in an index of NY passengers in a book in the IGSI library (Irish Genealogical Society Intl.) in St. Paul, MN. I'm from Portland, OR but I was visiting there doing the basic groundwork on this ancestor because that's where he settled after immigration, had his family and eventually died.
The biggest problem with passenger list indexes is that they usually give you TOO MANY people with the correct name, but in this case you know NY and 1851, so that narrows down the number of Patrick Kellys. I'd use one of the indexes (google on immigrant passenger lists or use ancestry.com) and list every Patrick Kelly that came through NY in 1851 for starters. One of those should be your ancestor. Sometimes to narrow it down you have to recognize who they were travelling with, which you may not know, but it's a start. That was why I asked about this topic. Just thought this was another person from the same part of Clare who arrived in NY in the same year.
One of the BEST resources is the Clare Library Online Genealgoy section at: http://www.clarelibrary.ie/eolas/coclare/genealogy/genealog.htm
Among other things in there you can search the various census substitutes for Kellys and if you find the right one, you'll have the townland, parish, barony, etc. all figured out.
The earliest one is the Freeholders List of 1821, which lists BOTH landowners AND tenants. In your case you'd be looking for his father (all these lists give only head of household's name unfortunately). Then you have a number of TIthe Applotment Lists from the 1830s, and Griffith's Valuation of about 1854, which will even give you a map of exactly where the land plot was. The trick was for me, and probably for you, is that my Mathias Breen was a boy living with his father until he emigrated, so he never appears on these lists. But fortunately I knew his father's name, and discovered in this process that Mathias was named for his grandfather (which was the rule for first born sons) who lived on the adjacent townland.
There's a whole bunch of other useful stuff in that Clare Library genealogy section, including lists of gravestones in local parish cemeteries. That, in my case, was how I clinched that this "other" Mathias I was turning up was in fact my great-grandfather's grandfather! After that, with the help of a local lady over there who's also researching her relation to Breens, I got parish church records, which are very spotty and incomplete but confirmed a few suspicions that had formed.
I think the Clare Library stuff is exceptionally helpful and I'd try to go through as much as I could before making a visit if I were you. You may make a real breakthrough and pinpoint exactly where the Kellys lived, like I did with the Breens.
Good luck to you, and be sure to post on here a report of your visit after you get back!