There is no doubt that most of the famous places in Sendai are located West of Sendai Station, and many short time visitors and tourists will go for this area.
BUT, if you are generally interested in shrines and temples you should probably go against the flow and leave the station at its back side to the West.
A map I found indicates no less than 35 shrines and temples in an area of 1x1 km, thus all in short walking distance.
Climb Mount Taihaku, the beautiful pyramid shaped mountain (or really just a large hill!) from which Taihaku ward in Sendai takes its name. I used to go there a lot - it was so peaceful. There are a couple of small shrines. You can reach the top without being spectacularly fit and although steep, there are chains to help pull yourself up. Once at the top you can see the ocean out to the west and some truly stunning views of the mountains to the south and east, particularly Zao. To get there, take a bus from Nagamachi Minami, one bound for Hitokita or Nihondaira, and the stop you want is Hitokita Chugakko Mae, you will find the path quite easily, and you will walk past Hitokita Junior High School on your left, where I once worked, rather unhappily - so thats why I used to walk up Taihaku as often as I could!!
At theOld Site of Sendai(Aoba) Castle, you can see this wonderful night view of Sendai City. You can often find some sailing ferries on the sea that you can see beyond the skycrapers.
Shopping for electronics in Japan is a very fun experience in itself... somewhat like visiting an art gallery; great designs & lots of choices! I love it!