What should I do?

I have a 1995 Chevy Monte Carlo. It has 157,000 miles on it. I am the second owner and it was maintained well by the 1st owner. The car is very quiet and has no leaks, smoke or anything like that. Two weeks ago I drove it over 600 miles to visit family. It was a nice smooth ride, but when I got about 100 miles from my destination I was going through a town (stop and go traffic) and I noticed that the car was resisting acceleration - it wouldn't shift into 2nd gear until the car reached 4 rpm (?). Anyway when I got home I got it checked out and was told that my transmission is on its way out. The car still drives and it drives well on the highway in the other gears. Anyway, my question is should I get the transmission fixed or just get a new car? I don't want to get a new car, but I'm afraid that because of the age of the car that it may be a beginning of other car problems. Please advise me on what is best to do.