Greer Garson was 51 when she made this movie, and still beautiful. I say "still" because in Hollywood in that era 40 was considered over-the-hill for a leading lady, so kudos to the studio for having her play the lead, and not someone's aunt or spinster older sister. Unfortunately, this movie doesn't have a lot going for it outside of Greer's considerable charm and acting ability. I'm a fan of Dana Andrews, but as others have noted, his acting style does not compliment Greer's, and his character is such a mean-spirited misogynistic jerk that it's hard not to intensely dislike him. Of course we know we're being set up for the ultimate romantic happy ending, but that's another issue with this movie. Everything is predictable.
Maybe the most interesting aspect of "Strange Lady in Town" is the chance to see a young Lois Smith in a major role. She went on to a very long, distinguished career as a character actress in movies and TV. (literally now in her 7th decade). Her 'Spurs' in "Strange Lady" is a little bit out there, but that's been true of many of her roles over the years. I recently saw her as an emotionally disturbed psychic on an episode of "Route 66" from the early '60s. She was a favorite of that show's producers, and made several appearances.