I'm from Tyler. There's not really a "city center". There is a downtown area, which is where Google drops you, but the surrounding area is mixed; some of it is fairly nice, and some of it is a bit run down (as you say). The downtown area mostly hosts legal stuff—courts, lawyers' offices, city government, etc.
South Tyler is generally considered to be somewhat nicer than the downtown area (which is further north). For instance, one of the nicer neighborhoods in Tyler is Holytree, which is off of Grande near its intersection with South Broadway. There are also some nice areas around the southern parts of Paluxy, which runs roughly parallel to Broadway. A lot of the nicer areas, though, are not actually within Tyler itself, but in the surrounding suburbs.
South Tyler is generally considered to be somewhat nicer than the downtown area (which is further north). For instance, one of the nicer neighborhoods in Tyler is Holytree, which is off of Grande near its intersection with South Broadway. There are also some nice areas around the southern parts of Paluxy, which runs roughly parallel to Broadway. A lot of the nicer areas, though, are not actually within Tyler itself, but in the surrounding suburbs.