Agree with previous two answers, if you go or return via New York City. Given your origination point, if you were connecting to the Lake Shore Limited in Chicago and getting off at Buffalo Depew station - the most direct route, the answer could be a bit different. For example, the LSL arrives around 9 in the morning and you would have quite a long wait for a train connection to Niagara Falls. Fortunately the Depew station is 5 minutes from the airport, with its assortment of hotels and perhaps of most use - rental cars.
Other rail options would involve travel through Canada using a combination of trains. There has been significant past discussion on all of the above, plus there are several here (including myself) who are very familiar with this area. With a few more details of your plans it would be easier to add suggestions.
Edited to add: Congratulations on your milestone anniversary as well!