Smith could have become an unrestricted free agent on July 1.
"I wouldn't say I was dead set on anything because it's the first time I've been in this position where I could talk to other teams and see the possibilities of other cities, but at the same time I really enjoyed my time with the Rangers so I had them at the top of the mountain if you want to say," said Smith, who mentioned he talked to between five and 10 teams but didn't want to name them. "We did talk to some teams, felt them out, saw what they would offer, and to me there was nothing that changed my mind enough from wanting to pursue four years with the Rangers."
The Rangers acquired Smith in a trade from the Detroit Red Wings on Feb. 28. He had nine points (three goals, six assists) in 51 games with the Rangers and Red Wings last season. He had four assists in 12 Stanley Cup Playoff games.
Smith said he felt comfortable with the Rangers' up-tempo style and likes that they are relatively young. New York has 10 players expected to be on the opening night roster, including restricted free agent forwards Mika Zibanejad and Jesper Fast, who are 26 or younger.
"I think I could be a big part of that team," Smith said. "I kind of like the niche that the Rangers have. They're a little bit younger. I noticed that we are ahead of what I expected the Rangers to be with all these young guys."
Smith also said a big reason for his comfort level in New York is the number of former college hockey players on the roster, including captain Ryan McDonagh, his former University of Wisconsin teammate from 2007-10.
Former Rangers center Derek Stepan, who was traded to the Arizona Coyotes last week, also played with Smith and McDonagh at Wisconsin.
Kevin Hayes (Boston College), Chris Kreider (Boston College), Jimmy Vesey (Harvard University), Steven Kampfer (University of Michigan) and Brady Skjei (University of Minnesota) also are NCAA products.
"Unfortunately Derek is on his way to Arizona, which is sad because we have a really close bond," Smith said. "But at the end of the day I still get to play with one of my best buddies and the captain, Ryan."
The Rangers like Smith because of the edge he plays with and his versatility as a left-handed defenseman who can play on the right side.
He played on the right this season after being traded to New York and likely will stay on that side, because the Rangers already have McDonagh, Skjei and Marc Staal on the left side.
New York may still add a right-handed defenseman through free agency.
"I can be versatile playing that side and I'm very comfortable," Smith said. "Definitely it was a bargaining chip on my side, and I think it helped. It worked too, because I thought Brady Skjei and I played pretty well together and he's really strong on his left side. So is a guy like Ryan McDonagh. I'm fine playing the left side on the penalty kill, but with having Ryan, Staal and Brady, it looks like I'll play the right side, and I'm totally comfortable with that."