Why locals love it?
Unlike Tallinn, Tartu has been somewhat less fortunate as far as medieval landmarks go. With little left standing, you'd have to use your imagination to fill in the blanks. And given that the town wall used to be 2 kilometres long and sporting 27 towers, there's a lot of blanks to fill.
Why you should visit it
If you're willing to spend an hour or two however, you can go for a small treasure hunt and discover the wall's remaining parts. Despite the relative lack of the wall's remains, it's still worth going around looking. The picturesque and quirky streets make for a sightseeing experience in it's own.
Look for the stone plates on the ground. They mark the nine gates which are all long gone by now.