Personally, I follow Don Draper's lead and use Canadian Club, but that's just because I prefer the taste to bourbons and ryes. To really follow the original recipe, rye is called for, and in that case I would use Old Overholt. But that's just me.
If you're looking to spend a bit more, I like Hudson's aptly named Manhattan Rye. 375ml will run you $40. You used to only be able to get it in NY (where I see you are), but it's becoming more common in nicer shops around here.
I like a Woodford Reserve old fashioned, but someone in another thread mentioned Old Forrester, which is made at the same distillery and costs less. I find the two taste close enough that I can't see any reason to buy Woodford Reserve.
I also enjoy Buffalo Trace bourbon.
For rye, I like Rittenhouse, but I have not made an old fashioned with it.
today i went to the two liquor stores we have in town, they didnt have bulleit rye or the old overholt i was looking for. so now trying to decide on a alternative
BWT...here's a twist on an Old Fashioned I learned recently (probably an old trick...but new to me). If you use Luxardo maraschino cherries, when you've used the last cherry add water to the remaining cherry syrup in a 1:1 ratio to make a cherry infused simple syrup, and then substitute this cherry simple syrup in the Old Fashioned recipe.
I started making Old Fashioned's about 2 years ago and I've made them with a number of Bourbons and a couple of Ryes since then. I prefer Bourbon for it, and my favorite Bourbon to make them with is Woodford Reserve.
I also have come to favor a particular recipe for the drink:
NO muddled fruits.
Cane sugar cube soaked with bitters crushed in the glass
Freshly frozen ice cubes made with good water
2 Shots of Woodford Reserve
Orange Peel Squeezed over the top for the oils in the peel, no squeezing of the meat inside
Garnished with more orange peel and a cherry
The drink comes out tasting more of Bourbon and less of fruit, nice and stout. Woodford isn't a super high % bottling, but it also doesn't produce a cocktail that tastes watered down unless it sits for a good bit longer than other bourbons would need to.
Got some Bulleit at a good price today at the local Bevmo so I decided to give it another run. I still prefer my Woodford Reserve Bourbon but this stuff is only barely behind it.